\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>11\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>8\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>11\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>11\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>11\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>19\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>19\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to isolate the \u003Ca href = \"#VARIABLE\">variable\u003C/a> in this \u003Ca href = \"#LINEAR\">linear\u003C/a> \u003Ca href = \"#EQUATION\">equation\u003C/a>, we need to get rid of the \u003Ca href = \"#COEFFICIENT\">coefficient\u003C/a> that multiplies it.\u003C/p>\u003Cp>This can be accomplished if both sides are divided by \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>19\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>19\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x={19}/{2}-->\n\u003C/div>\n \u003C/div> \u003C/div> ","x={19}/{2}","general","2x-11=8",{"row_html":82,"answer":83,"solver_type":79,"expression_latex":84,"expression":85}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 3 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>4\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C!-- FIRST-STEP-END -->\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> in this \u003Ca href = \"#TERM\">term\u003C/a> have been multiplied.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> in this \u003Ca href = \"#TERM\">term\u003C/a> have been multiplied.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>24\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>45\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: 45-->\n\u003C/div>\n \u003C/div> \u003C/div> ","45","\\left3cdot7right+\\left4cdot6right","3βˆ—7+4βˆ—6",{"row_html":87,"answer":88,"solver_type":79,"expression_latex":89,"expression":88}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 1 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='number'>10\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: sqrt10-->\n\u003C/div>\n \u003C/div> \u003C/div> ","sqrt10","\\sqrt{10}",{"row_html":91,"answer":92,"solver_type":79,"expression_latex":93,"expression":94}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 5 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/div>\u003C/div>\n\u003C!-- FIRST-STEP-END -->\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to \u003Ca href = \"#SOLVE\">solve\u003C/a> this \u003Ca href = \"#NON_LINEAR\">non-linear equation\u003C/a>, we need to move all the \u003Ca href = \"#TERM\">terms\u003C/a> to the left side.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp> - 3 terms \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, will be moved to the left side.\u003C/p>\u003Ccenter>\u003Cp>Notice that a term changes sign when it 'moves' from one side of the equation to the other.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to organize this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> into groups of \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a>, so we can combine them easier.\u003C/p>\u003C/center>\u003Cp>There are 3 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003C/p>\u003Cp>    third group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to combine \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> by adding up all numerical \u003Ca href = \"#COEFFICIENT\">coefficients\u003C/a> and copying the \u003Ca href = \"#LITERAL\">literal\u003C/a> part, if any.\u003C/p>\u003Cp>No numerical coefficient implies value of 1.\u003C/p>\u003C/center>\u003Cp>There are 3 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003C/p>\u003Cp>    third group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>0\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: y-6*{x}^{3}+3*{x}^{2}-2*x=0-->\n\u003C/div>\n\u003Cbr clear='both' />\u003Cbr clear='both' />\u003Cbr clear='both' />\n\u003Cdiv class=\"step \">\u003C!-- ESTART -->\u003Cdiv class=\"explanations\">\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' widht='100%' class='explanation_text'>\u003Ctbody>\u003Ctr>\n\u003Ctd valign='top' >\u003Cp>Explanation for this step does not exist.\u003C/p>\u003C/td>\n\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND --> ","y-6*{x}^{3}+3*{x}^{2}-2*x=0","y=6x3βˆ’3x2+2x","y=6x^3-3x^2+2x",{"row_html":96,"answer":97,"solver_type":79,"expression_latex":98,"expression":98}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 10 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/div>\u003C/div>\n\u003C!-- FIRST-STEP-END -->\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Simple numerical \u003Ca href = \"#TERM\">terms\u003C/a> are commonly written last.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to \u003Ca href = \"#SOLVE\">solve\u003C/a> this \u003Ca href = \"#LINEAR\">linear equation\u003C/a>, we need to group all the \u003Ca href = \"#VARIABLE\">variable\u003C/a> \u003Ca href = \"#TERM\">terms\u003C/a> on one side, and all the \u003Ca href = \"#CONSTANT\">constant\u003C/a> terms on the other side of the equation.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp> - term \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>21\u003C/span>\u003C/span>, will be moved to the right side.\u003C/p>\u003Cp> - term \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, will be moved to the left side.\u003C/p>\u003Ccenter>\u003Cp>Notice that a term changes sign when it 'moves' from one side of the equation to the other.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²numberβ€²>8\u003C/span>\u003Cvar>x\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cspanclass=β€²numberβ€²>5\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to organize this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> into groups of \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a>, so we can combine them easier.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>21\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to organize this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> into groups of \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a>, so we can combine them easier.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to combine \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> by adding up all numerical \u003Ca href = \"#COEFFICIENT\">coefficients\u003C/a> and copying the \u003Ca href = \"#LITERAL\">literal\u003C/a> part, if any.\u003C/p>\u003Cp>No numerical coefficient implies value of 1.\u003C/p>\u003C/center>\u003Ccenter>\u003Cp>Numerical 'like' \u003Ca href = \"#TERM\">terms\u003C/a> will be added.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>21\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to combine \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> by adding up all numerical \u003Ca href = \"#COEFFICIENT\">coefficients\u003C/a> and copying the \u003Ca href = \"#LITERAL\">literal\u003C/a> part, if any.\u003C/p>\u003Cp>No numerical coefficient implies value of 1.\u003C/p>\u003C/center>\u003Ccenter>\u003Cp>Numerical 'like' \u003Ca href = \"#TERM\">terms\u003C/a> will be added.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>10\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to isolate the \u003Ca href = \"#VARIABLE\">variable\u003C/a> in this \u003Ca href = \"#LINEAR\">linear\u003C/a> \u003Ca href = \"#EQUATION\">equation\u003C/a>, we need to get rid of the \u003Ca href = \"#COEFFICIENT\">coefficient\u003C/a> that multiplies it.\u003C/p>\u003Cp>This can be accomplished if both sides are divided by \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>10\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>10\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>10\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>10\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>10\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to reduce this \u003Ca href='#FRACTION'>fraction\u003C/a> we first need to write numerical \u003Ca href='#FACTOR_NOUN'>factors\u003C/a> as \u003Ca href='#PRODUCT'>products\u003C/a> of \u003Ca href='#PRIME'>primes\u003C/a>.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>     \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>16\u003C/span>\u003C/span> is rewritten as \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003Cp>     \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>10\u003C/span>\u003C/span> is rewritten as \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Let's multiply out the numbers after reduction.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003C/span> becomes \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>8\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>8\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x={8}/{5}-->\n\u003C/div>\n \u003C/div> \u003C/div> ","x={8}/{5}","21-2x=8x+5",{"row_html":100,"answer":101,"solver_type":79,"expression_latex":102,"expression":103}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 13 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan>log\u003C/span>\u003Csub>\u003Cspan class='number'>10\u003C/span>\u003C/sub>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='non-leaf s0'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='non-leaf s1'>\u003Cspan>log\u003C/span>\u003Csub>\u003Cspan class='number'>10\u003C/span>\u003C/sub>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²numberβ€²>4\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>10\u003C/span>\u003C/div>\u003C/div>\n\u003C!-- FIRST-STEP-END -->\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to \u003Ca href = \"#EVALUATE\">evaluate\u003C/a> a \u003Ca href = \"#POWER\">power\u003C/a> by multiplying the \u003Ca href = \"#BASE\">base\u003C/a> by itself as many times as the \u003Ca href = \"#EXPONENT\">exponent\u003C/a> indicates.\u003C/p>\u003Cp>In our example, base \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>7\u003C/span>\u003C/span> will be multiplied by itself twice.\u003C/p>\u003Ccenter>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We evaluate the logarithmic function.\u003C/p>\u003Cp>In other words, we substitute \u003Cspan class='formula rendered-math'>\u003Cvar>C\u003C/var>\u003C/span> for \u003Cspan class='formula rendered-math'>\u003Cspan>log\u003C/span>\u003Csub>\u003Cvar>A\u003C/var>\u003C/sub>\u003Cvar>B\u003C/var>\u003C/span>, in such a way that \u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003Csup class='non-leaf'>\u003Cvar>C\u003C/var>\u003C/sup>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>B\u003C/var>\u003C/span>.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>10\u003C/span>\u003C/span>,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>B\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>4\u003C/span>\u003C/span> and\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>C\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>0.60205999\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan>log\u003C/span>\u003Csub>\u003Cspan class='number'>10\u003C/span>\u003C/sub>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='non-leaf r0'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>0.60205999\u003C/span>\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>10\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of all the \u003Ca href = \"#DENOMINATOR\">denominators\u003C/a> in this \u003Ca href = \"#EQUATION\">equation\u003C/a>.\u003C/p>\u003Cp>This can be achieved by multiplying both the left and the right side by the \u003Ca href = \"#LEAST_COMMON_DENOMINATOR\">Least Common Denominator\u003C/a>.\u003C/p>\u003Cp>In our example, the \u003Ca href = \"#LCD\">LCD\u003C/a> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>0.60205999\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan>log\u003C/span>\u003Csub>\u003Cspan class='number'>10\u003C/span>\u003C/sub>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>0.60205999\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>10\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> in this \u003Ca href = \"#TERM\">term\u003C/a> have been multiplied.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan>log\u003C/span>\u003Csub>\u003Cspan class='number'>10\u003C/span>\u003C/sub>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>6.0205999\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to solve this logarithmic \u003Ca href = \"EQUATION\">equation\u003C/a>, we need to use that \u003Cspan class='formula rendered-math'>\u003Cspan>log\u003C/span>\u003Csub>\u003Cvar>a\u003C/var>\u003C/sub>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cvar>b\u003C/var>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>c\u003C/var>\u003C/span> is equivalent to \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003Csup class='non-leaf'>\u003Cvar>c\u003C/var>\u003C/sup>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>b\u003C/var>\u003C/span>.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>10\u003C/span>\u003C/span>,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>b\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span> and\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>c\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>6.0205999\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>10\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>6.0205999\u003C/span>\u003C/sup>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to \u003Ca href = \"#EVALUATE\">evaluate\u003C/a> a \u003Ca href = \"#POWER\">power\u003C/a> by multiplying the \u003Ca href = \"#BASE\">base\u003C/a> by itself as many times as the \u003Ca href = \"#EXPONENT\">exponent\u003C/a> indicates.\u003C/p>\u003Cp>In our example, base \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>10\u003C/span>\u003C/span> will be multiplied by itself six times.\u003C/p>\u003Ccenter>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>1048575.97\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to \u003Ca href = \"#SOLVE\">solve\u003C/a> this \u003Ca href = \"#LINEAR\">linear equation\u003C/a>, we need to group all the \u003Ca href = \"#VARIABLE\">variable\u003C/a> \u003Ca href = \"#TERM\">terms\u003C/a> on one side, and all the \u003Ca href = \"#CONSTANT\">constant\u003C/a> terms on the other side of the equation.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp> - term \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>, will be moved to the left side.\u003C/p>\u003Ccenter>\u003Cp>Notice that a term changes sign when it 'moves' from one side of the equation to the other.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>1048575.97\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>1048624.97\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>49\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>1048624.97\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In an \u003Ca href = \"#EQUATION\">equation\u003C/a>, the \u003Ca href = \"#VARIABLE\">variable\u003C/a> \u003Ca href = \"#TERM\">term\u003C/a> is commonly written on the left side.\u003C/p>\u003Cp>This can be done by switching the sides of the equation.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>1048624.97\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to isolate the \u003Ca href = \"#VARIABLE\">variable\u003C/a> in this \u003Ca href = \"#LINEAR\">linear\u003C/a> \u003Ca href = \"#EQUATION\">equation\u003C/a>, we need to get rid of the \u003Ca href = \"#COEFFICIENT\">coefficient\u003C/a> that multiplies it.\u003C/p>\u003Cp>This can be accomplished if both sides are divided by \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>1048624.97\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>1048624.97\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In this \u003Ca href = \"#FRACTION\">fraction\u003C/a>, the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> 1048624.97 has been divided by the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a> 3.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>349541.657\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x=349541.657-->\n\u003C/div>\n \u003C/div> \u003C/div> ","x=349541.657","log(3xβˆ’7^2)/log4=10","log3xβˆ’72/log4=10",{"row_html":105,"answer":106,"solver_type":79,"expression_latex":107,"expression":108}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 14 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>10\u003C/span>\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/div>\u003C/div>\n\u003C!-- FIRST-STEP-END -->\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to \u003Ca href = \"#FACTOR_VERB\">factor\u003C/a> an \u003Ca href = \"#INTEGER\">integer\u003C/a>, we need to repeatedly \u003Ca href = \"#DIVIDEND\">divide\u003C/a> it by the ascending sequence of \u003Ca href = \"#PRIME\">primes\u003C/a> 2,3,5....\u003C/p>\u003Cp>The number of times that each prime divides the original integer becomes its \u003Ca href = \"#EXPONENT\">exponent\u003C/a> in the final result.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>     Prime number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span> to the power of \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>1\u003C/span>\u003C/span> equals \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003Cp>     Prime number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span> to the power of \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>1\u003C/span>\u003C/span> equals \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>5\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to \u003Ca href = \"#FACTOR_VERB\">factor\u003C/a> out the \u003Ca href = \"#GREATEST_COMMON_FACTOR\">GCF\u003C/a> GreatestCommonFactor.\u003C/p>\u003Cp>The resulting \u003Ca href = \"#TERM\">term\u003C/a> is a \u003Ca href = \"#PRODUCT\">product\u003C/a> of the GCF and the original \u003Ca href = \"#EXPRESSION\">expression\u003C/a> divided by the GCF.\u003C/p>\u003Cp>In our example, the GCF is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>5\u003C/span>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf s2'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>(\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r2'>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>)\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to solve this \u003Ca href = \"#NON_LINEAR\">non-linear\u003C/a> \u003Ca href = \"#EQUATION\">equation\u003C/a>, we will apply the \u003CA href=\"#ZERO_PRODUCT_THEOREM\">zero product theorem\u003C/a>.\u003C/p>\u003Cp>That means that each \u003Ca href = \"#VARIABLE\">variable\u003C/a> \u003Ca href = \"#FACTOR_NOUN\">factor\u003C/a> in the original equation needs to be set to zero.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Before \u003Ca href = \"#FACTOR_VERB\">factoring\u003C/a> this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> as a \u003Ca href = \"#SQUARE\">square\u003C/a> of \u003Ca href = \"#BINOMIAL\">binomial\u003C/a>, we first need to make A and B in the following expression \u003Ca href = \"#EXPLICIT_VARIABLE\">explicit\u003C/a>:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>A\u003C/var>\u003Cvar>B\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cvar>B\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cvar>x\u003C/var>\u003C/span> and\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>B\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to \u003Ca href = \"#FACTOR_VERB\">factor\u003C/a> this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> as a \u003Ca href = \"#SQUARE\">square\u003C/a> of \u003Ca href = \"#BINOMIAL\">binomial\u003C/a>, by applying the following rule:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>A\u003C/var>\u003Cvar>B\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cvar>B\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cvar>A\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cvar>B\u003C/var>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>.\u003C/p>\u003Cp>In our example,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cvar>x\u003C/var>\u003C/span> and\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>B\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In this \u003Ca href = \"#NON_LINEAR\">non-linear\u003C/a> \u003Ca href = \"#EQUATION\">equation\u003C/a>, the \u003Ca href = \"#VARIABLE\">variable\u003C/a> needs to be isolated.\u003C/p>\u003Cp>This is accomplished when both sides are \u003Ca href = \"#EXPONENTIATE\">exponentiated\u003C/a> by the \u003Ca href = \"#RECIPROCAL\">reciprocal\u003C/a> of the variable's \u003Ca href = \"#EXPONENT\">exponent\u003C/a>.\u003C/p>\u003C/center>\u003Cp>In our example, this reciprocal is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/p>\u003Cp>Notice that since the exponent we applied has an even \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>, two solutions should have been created.\u003C/p>\u003Cp>However, since we are exponentiating number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>0\u003C/span>\u003C/span>, only one solution is created.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>(\u003C/span>\u003Cspan class='non-leaf'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003Cspan class='scaled paren'>)\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/sup>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to \u003Ca href = \"#EXPONENTIATE\">exponentiate\u003C/a> the \u003Ca href = \"#POWER\">power\u003C/a>.\u003C/p>\u003Cp>The following rule is applied:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cvar>A\u003C/var>\u003Csupclass=β€²nonβˆ’leafβ€²>\u003Cvar>B\u003C/var>\u003C/sup>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cvar>C\u003C/var>\u003C/sup>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>A\u003C/var>\u003Csup class='non-leaf'>\u003Cvar>B\u003C/var>\u003Cvar>C\u003C/var>\u003C/sup>\u003C/span>\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>B\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span> and\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>C\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/sup>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to perform a multiplication.\u003C/p>\u003Cp>The following rule is applied:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>A\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cvar>B\u003C/var>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003Cvar>C\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>A\u003C/var>\u003Cvar>C\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cvar>B\u003C/var>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/p>\u003Cp>In our example, the \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> in the new \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> are:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>1\u003C/span>\u003C/span>,\u003C/p>\u003Cp>Notice that all non-fraction factors are placed in the numerator.\u003C/p>\u003Cp>The only factor in the new \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a> is:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cvar>x\u003C/var>\u003Cspan class='non-leaf r0'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>0\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to \u003Ca href = \"#SOLVE\">solve\u003C/a> this \u003Ca href = \"#LINEAR\">linear equation\u003C/a>, we need to group all the \u003Ca href = \"#VARIABLE\">variable\u003C/a> \u003Ca href = \"#TERM\">terms\u003C/a> on one side, and all the \u003Ca href = \"#CONSTANT\">constant\u003C/a> terms on the other side of the equation.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp> - term \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>, will be moved to the right side.\u003C/p>\u003Ccenter>\u003Cp>Notice that a term changes sign when it 'moves' from one side of the equation to the other.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x=1-->\n\u003C/div>\n \u003C/div> \u003C/div> ","x=1","5x2βˆ’10x+5=0","5x^2-10x+5=0",{"row_html":110,"answer":111,"solver_type":79,"expression_latex":112,"expression":112}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 1 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cvar>x\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cvar>y\u003C/var>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: {x}^{2}+y+2*x*y-->\n\u003C/div>\n \u003C/div> \u003C/div> ","{x}^{2}+y+2*x*y","x^2+y+2xy",{"row_html":114,"answer":115,"solver_type":79,"expression_latex":116,"expression":117}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 4 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cvar>a\u003C/var>\u003Cvar>c\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>m\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>n\u003C/var>\u003Cvar>y\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>l\u003C/var>\u003Cvar>l\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>y\u003C/var>\u003Cvar>l\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>b\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>l\u003C/var>\u003Cspan class='nonSymbola constant'>π\u003C/span>\u003Cvar>n\u003C/var>\u003Cvar>s\u003C/var>\u003C/span>\u003C/div>\u003C/div>\n\u003C!-- FIRST-STEP-END -->\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to organize this \u003Ca href = \"#TERM\">term\u003C/a> into groups of \u003Ca href = \"#LIKE_FACTORS\">like factors\u003C/a>, so we can combine them easier.\u003C/p>\u003C/center>\u003Cp>The following are like factors:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003C/span>\u003C/p>\u003Cp>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cvar>o\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>o\u003C/var>\u003C/span>\u003C/p>\u003Cp>\u003C/p>\u003Cp>    third group: \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fourth group: \u003Cspan class='formula rendered-math'>\u003Cvar>n\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>n\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fifth group: \u003Cspan class='formula rendered-math'>\u003Cvar>y\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>y\u003C/var>\u003C/span>\u003C/p>\u003Cp>    sixth group: \u003Cspan class='formula rendered-math'>\u003Cvar>s\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>s\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>s\u003C/var>\u003C/span>\u003C/p>\u003Cp>    seventh group: \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>\u003C/p>\u003Cp>    eighth group: \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>\u003C/p>\u003Cp>\u003C/p>\u003Cp>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cvar>a\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>c\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>m\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>p\u003C/var>\u003Cvar>n\u003C/var>\u003Cvar>n\u003C/var>\u003Cvar>y\u003C/var>\u003Cvar>y\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>l\u003C/var>\u003Cvar>l\u003C/var>\u003Cvar>l\u003C/var>\u003Cvar>l\u003C/var>\u003Cvar>b\u003C/var>\u003Cspan class='nonSymbola constant'>π\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to combine \u003Ca href = \"#LIKE_FACTORS\">like factors\u003C/a> in this \u003Ca href = \"#TERM\">term\u003C/a> by adding up all the \u003Ca href = \"#EXPONENT\">exponents\u003C/a> and copying the \u003Ca href = \"#BASE\">base\u003C/a>.\u003C/p>\u003Cp>No exponent implies the value of 1.\u003C/p>\u003C/center>\u003Cp>The following are like factors:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>a\u003C/var>\u003C/span>\u003C/p>\u003Cp>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cvar>o\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>o\u003C/var>\u003C/span>\u003C/p>\u003Cp>\u003C/p>\u003Cp>    third group: \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>p\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fourth group: \u003Cspan class='formula rendered-math'>\u003Cvar>n\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>n\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fifth group: \u003Cspan class='formula rendered-math'>\u003Cvar>y\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>y\u003C/var>\u003C/span>\u003C/p>\u003Cp>    sixth group: \u003Cspan class='formula rendered-math'>\u003Cvar>s\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>s\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>s\u003C/var>\u003C/span>\u003C/p>\u003Cp>    seventh group: \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>\u003C/p>\u003Cp>    eighth group: \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>l\u003C/var>\u003C/span>\u003C/p>\u003Cp>\u003C/p>\u003Cp>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>a\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>c\u003C/var>\u003Cvar>o\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>m\u003C/var>\u003Cvar>p\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s2'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>n\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s3'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>y\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s4'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>s\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s5'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>e\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s6'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>l\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s7'>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>b\u003C/var>\u003Cspan class='nonSymbola constant'>π\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> have been added.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cvar>a\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>c\u003C/var>\u003Cvar>o\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>m\u003C/var>\u003Cvar>p\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r2'>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>n\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r3'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>y\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r4'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>s\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r5'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>e\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r6'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>l\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r7'>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>b\u003C/var>\u003Cspan class='nonSymbola constant'>π\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: {a}^{3}*c*{o}^{2}*m*{p}^{4}*{n}^{2}*{y}^{2}*{s}^{3}*{e}^{2}*{l}^{4}*b*pi-->\n\u003C/div>\n \u003C/div> \u003C/div> ","{a}^{3}*c*{o}^{2}*m*{p}^{4}*{n}^{2}*{y}^{2}*{s}^{3}*{e}^{2}*{l}^{4}*b*pi","acompanysellspoppylabelp\\in s","acompanysellspoppylabelp in s",{"row_html":119,"answer":120,"solver_type":79,"expression_latex":121,"expression":122}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 14 -->\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003C!-- FIRST-STEP-EXPLANATIONS -->\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003C/div>\u003C/div>\n\u003C!-- FIRST-STEP-END -->\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to perform a multiplication.\u003C/p>\u003Cp>The following rule is applied:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>A\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cvar>B\u003C/var>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003Cvar>C\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>A\u003C/var>\u003Cvar>C\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cvar>B\u003C/var>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/p>\u003Cp>In our example, the \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> in the new \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> are:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>1\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>x\u003C/var>\u003C/span>,\u003C/p>\u003Cp>Notice that all non-fraction factors are placed in the numerator.\u003C/p>\u003Cp>The only factor in the new \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a> is:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to add \u003Ca href='#FRACTION'>fractions\u003C/a>, we first have to rewrite them so that they all have the same common \u003Ca href='#DENOMINATOR'>denominator\u003C/a>.\u003C/p>\u003Cp>We will make fractions' \u003Ca href='#DENOMINATOR'>denominators\u003C/a> equivalent by finding the \u003Ca href='#LCD'>LCD\u003C/a> of all fractions and then multiplying both the \u003Ca href='#NUMERATOR'>numerator\u003C/a> and \u003Ca href='#DENOMINATOR'>denominator\u003C/a> of each \u003Ca href='#FRACTION'>fraction\u003C/a> by \u003Ca href='#FACTOR_NOUN'>factors\u003C/a> that are missing in the \u003Ca href='#DENOMINATOR'>denominator\u003C/a>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to add a non-fractional \u003Ca href='#TERM'>term\u003C/a> to a \u003Ca href='#FRACTION'>fraction\u003C/a>, we first need to convert it into a \u003Ca href='#FRACTION'>fraction\u003C/a>, by creating a \u003Ca href='#DENOMINATOR'>denominator\u003C/a> that is equal to 1.\u003C/p>\u003Cp>Then we need to multiply both the \u003Ca href='#NUMERATOR'>numerator\u003C/a> and the \u003Ca href='#DENOMINATOR'>denominator\u003C/a> of the newly created \u003Ca href='#FRACTION'>fraction\u003C/a> by the \u003Ca href='#LEAST_COMMON_DENOMINATOR'>LCD\u003C/a> of all fractions that are being added.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>\u003Ca href='#LCD'>LCD\u003C/a> is equal to:\u003C/p>\u003Ccenter>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to add \u003Ca href='#FRACTION'>fractions\u003C/a> that have a common \u003Ca href='#DENOMINATOR'>denominator\u003C/a>. The \u003Ca href='#NUMERATOR'>numerator\u003C/a> of the the newly created fraction will be the sum of all the existing \u003Ca href='#NUMERATOR'>numerators\u003C/a>, and its \u003Ca href='#DENOMINATOR'>denominator\u003C/a> will be equal to the common \u003Ca href='#DENOMINATOR'>denominator\u003C/a>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> in this \u003Ca href = \"#TERM\">term\u003C/a> have been multiplied.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of all the \u003Ca href = \"#DENOMINATOR\">denominators\u003C/a> in this \u003Ca href = \"#EQUATION\">equation\u003C/a>.\u003C/p>\u003Cp>This can be achieved by multiplying both the left and the right side by the \u003Ca href = \"#LEAST_COMMON_DENOMINATOR\">Least Common Denominator\u003C/a>.\u003C/p>\u003Cp>In our example, the \u003Ca href = \"#LCD\">LCD\u003C/a> is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to \u003Ca href = \"#EXPAND\">expand\u003C/a> this \u003Ca href = \"#TERM\">term\u003C/a> by multiplying a term and an \u003Ca href = \"#EXPRESSION\">expression\u003C/a>.\u003C/p>\u003Cp>The following \u003Ca href = \"#PRODUCT\">product\u003C/a> distributive property will be used:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cvar>A\u003C/var>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cvar>B\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cvar>C\u003C/var>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>A\u003C/var>\u003Cvar>B\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cvar>A\u003C/var>\u003Cvar>C\u003C/var>\u003C/span>.\u003C/p>\u003C/center>\u003Cp>In our example, the resulting expression will consist of 2 terms:\u003C/p>\u003Cp>    the first term is a product of \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span> and \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>.\u003C/p>\u003Cp>    the second term is a product of \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span> and \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>8\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>8\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>4\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> in this \u003Ca href = \"#TERM\">term\u003C/a> have been multiplied.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to \u003Ca href = \"#SOLVE\">solve\u003C/a> this \u003Ca href = \"#LINEAR\">linear equation\u003C/a>, we need to group all the \u003Ca href = \"#VARIABLE\">variable\u003C/a> \u003Ca href = \"#TERM\">terms\u003C/a> on one side, and all the \u003Ca href = \"#CONSTANT\">constant\u003C/a> terms on the other side of the equation.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp> - term \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>16\u003C/span>\u003C/span>, will be moved to the right side.\u003C/p>\u003Cp> - term \u003Cspan class='formula rendered-math'>\u003Cvar>x\u003C/var>\u003C/span>, will be moved to the left side.\u003C/p>\u003Ccenter>\u003Cp>Notice that a term changes sign when it 'moves' from one side of the equation to the other.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cvar>x\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cspanclass=β€²numberβ€²>4\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to get rid of \u003Ca href = \"#EXPRESSION\">expression\u003C/a> parentheses.\u003C/p>\u003Cp>If there is a negative sign in front of it, each \u003Ca href = \"#TERM\">term\u003C/a> within the expression changes sign.\u003C/p>\u003Cp>Otherwise, the expression remains unchanged.\u003C/p>\u003Ccenter>\u003Cp>In our example, there are no negative expressions.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf s1'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>4\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to organize this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> into groups of \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a>, so we can combine them easier.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>16\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to organize this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> into groups of \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a>, so we can combine them easier.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>4\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf s1'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>4\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to combine \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> by adding up all numerical \u003Ca href = \"#COEFFICIENT\">coefficients\u003C/a> and copying the \u003Ca href = \"#LITERAL\">literal\u003C/a> part, if any.\u003C/p>\u003Cp>No numerical coefficient implies value of 1.\u003C/p>\u003C/center>\u003Ccenter>\u003Cp>Numerical 'like' \u003Ca href = \"#TERM\">terms\u003C/a> will be added.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>16\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to combine \u003Ca href = \"#LIKE_TERMS\">like terms\u003C/a> in this \u003Ca href = \"#EXPRESSION\">expression\u003C/a> by adding up all numerical \u003Ca href = \"#COEFFICIENT\">coefficients\u003C/a> and copying the \u003Ca href = \"#LITERAL\">literal\u003C/a> part, if any.\u003C/p>\u003Cp>No numerical coefficient implies value of 1.\u003C/p>\u003C/center>\u003Ccenter>\u003Cp>Numerical 'like' \u003Ca href = \"#TERM\">terms\u003C/a> will be added.\u003C/p>\u003C/center>\u003Cp>There are 2 groups of like terms:\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cvar>x\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>4\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>16\u003C/span>\u003C/span>\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf r0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>12\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>In order to isolate the \u003Ca href = \"#VARIABLE\">variable\u003C/a> in this \u003Ca href = \"#LINEAR\">linear\u003C/a> \u003Ca href = \"#EQUATION\">equation\u003C/a>, we need to get rid of the \u003Ca href = \"#COEFFICIENT\">coefficient\u003C/a> that multiplies it.\u003C/p>\u003Cp>This can be accomplished if both sides are divided by \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>12\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\u003C/div>\n\u003Cdiv class='step'>\u003C!-- ESTART -->\u003Cdiv class='explanations'>\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We need to reduce this \u003Ca href = \"#FRACTION\">fraction\u003C/a> to the lowest \u003Ca href = \"#TERM\">terms\u003C/a>.\u003C/p>\u003Cp>This can be done by dividing out those \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear both in the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> and in the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a>.\u003C/p>\u003Cp>In our example, this is the common factor:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003C/span>.\u003C/p>\u003C/center>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003Cdiv style='display:none' class='substep notinited' >\u003Ctable cellpadding='0' cellspacing='0' class='explanation_text ' >\u003Ctbody>\u003Ctr>\u003Ctd>\u003Ccenter>\u003Cp>We can reduce this \u003Ca href='#FRACTION'>fraction\u003C/a> by dividing both \u003Ca href='#NUMERATOR'>numerator\u003C/a> and \u003Ca href='#DENOMINATOR'>denominator\u003C/a> by a common numeric \u003Ca href='#FACTOR_NOUN'>factors\u003C/a>.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>    both number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>12\u003C/span>\u003C/span> in numerator and number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003C/span> in denominator are divisible by \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003C/span>.\u003C/p>\u003C/td>\u003C/tr>\u003C/table>\u003C/div>\n\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x=4-->\n\u003C/div>\n \u003C/div> \u003C/div> ","x=4","-x+8=\\frac12x+2","-x+8=1/2x+2",{"data":124},[125,128,131,135,138,141,144,147],{"id":48,"h1":126,"slug":127},"Math Word Problem Solver","math-word-problem-solver",{"id":61,"h1":129,"slug":130},"Math Calculus Solver","math-calculus-solver",{"id":132,"h1":133,"slug":134},7,"Math Fill In The Blank Solver","math-fill-in-the-blank-solver",{"id":64,"h1":136,"slug":137},"Math Story Problem Solver","math-story-problem-solver",{"id":52,"h1":139,"slug":140},"Geometry Math Solver","geometry-math-solver",{"id":58,"h1":142,"slug":143},"Best Math Problem Solver App","best-math-problem-solver-app",{"id":55,"h1":145,"slug":146},"Math Word Problem Solver App","math-word-problem-solver-app",{"id":148,"h1":149,"slug":150},8,"Math Sequence 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