.\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'>3\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'>3\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'>2\u003C/span>\u003C/span> equals \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>25\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>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'>3\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'>3\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\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>\u003Cp>     Prime number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>7\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'>7\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'>\u003Ctable class='forest' cellspacing='0' cellpadding='0'>\u003Ctbody>\u003Ctr>\u003Ctd>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003C/td>\u003Ctd>\u003Cspan class=\"binary-operator\">,\u003C/span>\u003C/td>\u003Ctd>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003C/td>\u003Ctd>\u003Cspan class=\"binary-operator\">,\u003C/span>\u003C/td>\u003Ctd>\u003Cspan class='non-leaf r2'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003C/td>\u003C/tr>\u003C/tbody>\u003C/table>\u003C!--//FOREST-->\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>The \u003Ca href = \"#LCD\">LCM\u003C/a> is constructed by multiplying all the \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> that appear in any of the given \u003Ca href = \"#EXPRESSION\">expressions\u003C/a>, \u003Ca href = \"#EXPONENTIATE\">exponentiated\u003C/a> to the largest \u003Ca href = \"#POWER\">power\u003C/a>.\u003C/p>\u003Cp>In our example, all the factors are: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>5\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003C/p>\u003Cp>Therefore, the LCM is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>5\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'>7\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'>5\u003C/span>\u003C/span> will be multiplied by itself twice.\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='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>25\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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 r0'>\u003Cspan class='number'>1050\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: 1050-->\n\u003C/div>\n \u003C/div> \u003C/div> ","1050","lcm","150,30,70",{"row_html":82,"answer":83,"solver_type":84,"expression_latex":85,"expression":85}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 9 -->\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'>7\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>4\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>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'>6\u003C/span>\u003Cvar>y\u003C/var>\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>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²numberβ€²>7\u003C/span>\u003Cvar>x\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cspanclass=β€²numberβ€²>6\u003C/span>\u003Cvar>y\u003C/var>\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'>6\u003C/span>\u003Cvar>y\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='number'>4\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>y\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'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>7\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>y\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'>4\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>y\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 is only one group of like terms:\u003C/p>\u003Cp>\u003C/p>\u003Cp>     \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>6\u003C/span>\u003Cvar>y\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>y\u003C/var>\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>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 class='number'>7\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>4\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'>7\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'>7\u003C/span>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>7\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>−\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>6\u003C/span>\u003C/span>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf s2'>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>7\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'>7\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 \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'>3\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'>3\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>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'>2\u003C/span>\u003C/span> equals \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>4\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='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cspan class='non-leaf r1'>\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'>3\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cvar>y\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r2'>\u003Cspan class='number'>2\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width: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 = \"#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'>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='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\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'>3\u003C/span>\u003Cvar>y\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='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\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>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width: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 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\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'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan>−\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>(\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cvar>y\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>2\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width: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 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>\u003Cp>In our example, the following 2 terms will change sign:\u003C/p>\u003C/center>\u003Ccenter>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>3\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>y\u003C/var>\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>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'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>3\u003C/span>\u003Cvar>y\u003C/var>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x={2*βˆ’3βˆ—y+2}/{7}-->\n\u003C/div>\n \u003C/div> \u003C/div> ","x={2*βˆ’3βˆ—y+2}/{7}","general","7x+6y=4",{"row_html":87,"answer":88,"solver_type":89,"expression_latex":90,"expression":91}," \u003Cdiv> \u003Ch3>Simplify\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 7 -->\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'>32\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>92\u003C/span>\u003C/span>\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>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'>2\u003C/span>\u003C/span> equals \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>4\u003C/span>\u003C/span>.\u003C/p>\u003Cp>     Prime number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>23\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'>23\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='number'>32\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>2\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>23\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 \u003Ca href = \"#DISTRIBUTE\">distribute\u003C/a> the \u003Ca href = \"#RADICAL\">radical\u003C/a> sign over each \u003Ca href = \"#FACTOR_NOUN\">factor\u003C/a> in the \u003Ca href = \"#TERM\">term\u003C/a>.\u003C/p>\u003Cp>The following rule is applied:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='scaled'>\u003Csup class='nthroot non-leaf'>\u003Cvar>C\u003C/var>\u003C/sup>\u003Cspan class='sqrt-prefix scaled'>√\u003C/span>\u003Cspan class='sqrt-stem non-leaf'>\u003Cvar>A\u003C/var>\u003Cvar>B\u003C/var>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='scaled'>\u003Csup class='nthroot non-leaf'>\u003Cvar>C\u003C/var>\u003C/sup>\u003Cspan class='sqrt-prefix scaled'>√\u003C/span>\u003Cspan class='sqrt-stem non-leaf'>\u003Cvar>A\u003C/var>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='scaled'>\u003Csup class='nthroot non-leaf'>\u003Cvar>C\u003C/var>\u003C/sup>\u003Cspan class='sqrt-prefix scaled'>√\u003C/span>\u003Cspan class='sqrt-stem non-leaf'>\u003Cvar>B\u003C/var>\u003C/span>\u003C/span>\u003C/span>\u003C/p>\u003Cp>In our example, the \u003Ca href = \"#RADICAL_INDEX\">radical index\u003C/a> \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span> is distributed over each factor of \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>23\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='number'>32\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf s0'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='number'>2\u003C/span>\u003Csup class='non-leaf'>\u003Cspan class='number'>2\u003C/span>\u003C/sup>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='number'>23\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\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 can \u003Ca href = \"#SIMPLIFY\">simplify\u003C/a> a \u003Ca href = \"#RADICAL\">radical\u003C/a> by removing the \u003Ca href = \"#GCF\">GCF\u003C/a> between the \u003Ca href = \"#EXPONENT\">exponent\u003C/a> in the \u003Ca href = \"#RADICAND\">radicand\u003C/a> and the \u003Ca href = \"#RADICAL_INDEX\">radical index\u003C/a>.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>     the exponent in the radicand is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>,\u003C/p>\u003Cp>     the radical index is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span> and\u003C/p>\u003Cp>     the greatest common factor is equal to \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003Cp>Since the \u003Ca href = \"#GCF\">GCF\u003C/a> is equal to the radical index, we can completely remove the radical sign.\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='number'>32\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>2\u003C/span>\u003Csup class='non-leaf'>\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/sup>\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='number'>23\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\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'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>32\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='number'>23\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\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 parentheses in this \u003Ca href = \"#TERM\">term\u003C/a>.\u003C/p>\u003Cp>All the negative \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> will change sign.\u003C/p>\u003Cp>In our example, we do not have any negative factors.\u003C/p>\u003Cp>The sign of the term will not change.\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'>32\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='number'>23\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>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 r0'>\u003Cspan class='number'>64\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled sqrt-prefix'>√\u003C/span>\u003Cspan class='non-leaf sqrt-stem'>\u003Cspan class='number'>23\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: 64*sqrt23-->\n\u003C/div>\n \u003C/div> \u003C/div> ","64*sqrt23","simplify","32\\sqrt{92}","32sqrt92",{"row_html":93,"answer":94,"solver_type":89,"expression_latex":95,"expression":95}," \u003Cdiv> \u003Ch3>Simplify\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 11 -->\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>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>62\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>38\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='number'>90\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>In order to bring this \u003Ca href = \"#EQUATION\">equation\u003C/a> to \u003Ca href = \"#GRAPHABLE_FORM\">graphable form\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> - term \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>90\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 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>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cvar>x\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cspanclass=β€²numberβ€²>62\u003C/span>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cvar>x\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cspanclass=β€²numberβ€²>38\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'>90\u003C/span>\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='number'>90\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'>90\u003C/span>\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'>\u003Cspan class='non-leaf s0'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>62\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>38\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>90\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'>90\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>90\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 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'>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>62\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>38\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>90\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>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'>\u003Cspan class='non-leaf s0'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>62\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>38\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>90\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r1'>\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 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'>\u003Cvar>x\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>62\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>38\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='number'>90\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='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>10\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 class='number'>10\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>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²numberβ€²>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspanclass=β€²binaryβˆ’operatorβ€²>+\u003C/span>\u003Cspanclass=β€²numberβ€²>10\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'>10\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\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 \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'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>10\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>10\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>10\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='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>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>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>10\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/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 rewrite the \u003Ca href = \"#EQUATION\">equation\u003C/a> of this \u003Ca href = \"#LINE\">line\u003C/a> in a \u003Ca href = \"#GRAPHABLE_FORM\">graphable form\u003C/a>. \u003C/center>\u003Ccenter>\u003Cp>This can be accomplished by \u003Ca href = \"#SIMPLIFY\">simplifying\u003C/a> the left side and making the \u003Ca href = \"#COEFFICIENT\">coefficients\u003C/a> on the right side \u003Ca href = \"#EXPLICIT_COEFFICIENT\">explicit\u003C/a>.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>     the coefficient of the variable term is equal to \u003Cspan class='formula rendered-math'>\u003Cspan>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>10\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 odd'>\u003Cdiv class='rendered-math'>\u003Cspan class='non-leaf r0'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>10\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/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 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'>10\u003C/span>\u003C/span> in numerator and number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span> in denominator are divisible by \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\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'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²numberβ€²>5\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x=-5-->\n\u003C/div>\n\u003Cbr clear='both' />\u003Cbr clear='both' />\u003Cdiv style='white-space: normal ; padding:5px ; box-shadow: 1px 1px 2px #000000; border-radius: 5px; margin:0 5px ; ' class='fullWidth'>\u003C/p>\u003C/div>\u003Cbr clear='both' />\n \u003C/div> \u003C/div> ","x=-5","x+62+x+38=90",{"row_html":97,"answer":98,"solver_type":84,"expression_latex":99,"expression":100}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 11 -->\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>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan>tan\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²numberβ€²>10\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>180\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>The trigonometric function has been evaluated with the assumption that the argument is given in degrees.\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>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>0.17632698\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>180\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 convert this non-repeating decimal into a \u003Ca href = \"#RATIONAL\">rational\u003C/a> number.\u003C/p>\u003Cp>This can be accomplished by rewriting the given number as a \u003Ca href = \"#FRACTION\">fraction\u003C/a>, where the \u003Ca href = \"#NUMERATOR\">numerator\u003C/a> is equal to the number after the decimal point, and the \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a> is equal to \u003Cspan class='formula rendered-math'>\u003Cvar>10\u003C/var>\u003Csup class='non-leaf'>\u003Cvar>n\u003C/var>\u003C/sup>\u003C/span>, where n is the number of decimal places.\u003C/p>\u003C/center>\u003Cp>In our example,\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>n\u003C/var>\u003C/span> is equal to \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'>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>17632698\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>100000000\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>180\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 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'>17632698\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2938783\u003C/span>\u003C/span>.\u003C/p>\u003Cp>     \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>100000000\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>\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>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\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'>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='non-leaf r0'>\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2938783\u003C/span>\u003C/span>\u003Cspan class='denominator'>\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>\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>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\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>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>180\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>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2938783\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='non-leaf s1'>\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>\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>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\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='number'>180\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2938783\u003C/span>\u003C/span> becomes \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>8816349\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>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>\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>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>2\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>5\u003C/span>\u003C/span> becomes \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>50000000\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'>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>8816349\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>50000000\u003C/span>\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='number'>180\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'>\u003Cvar>a\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>r\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>c\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>8816349\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'>50000000\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='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf s0'>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>8816349\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>50000000\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='number'>180\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> are commonly written first.\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='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>8816349\u003C/span>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>50000000\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 s1'>\u003Cspan class='number'>180\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'>50000000\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'>8816349\u003C/span>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>50000000\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'>180\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>50000000\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>50000000\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 class='non-leaf r0'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>8816349\u003C/span>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>180\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>50000000\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>50000000\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'>\u003C/div>\n\u003C!-- EEND -->\u003Cdiv class='step-result even'>\u003Cdiv class='rendered-math'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>8816349\u003C/span>\u003Cvar>a\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>c\u003C/var>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class=\"undefined-op\">\u003Cspan class='number'>180\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>50000000\u003C/span>\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>50000000\u003C/span>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: {8816349*a*r*c+180*50000000}/{50000000}-->\n\u003C/div>\n \u003C/div> \u003C/div> ","{8816349*a*r*c+180*50000000}/{50000000}","\\arctan\\left10right+180","arctan 10+180",{"row_html":102,"answer":103,"solver_type":89,"expression_latex":104,"expression":105}," \u003Cdiv> \u003Ch3>Simplify\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>w\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>i\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>h\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>i\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>f\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>6\u003C/span>\u003Cvar>w\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>k\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>o\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>12\u003C/span>\u003Cvar>d\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>y\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>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#TERM\">terms\u003C/a> are commonly written first.\u003C/p>\u003C/center>\u003Cp>The following are like factors:\u003C/p>\u003Cp>\u003C/p>\u003Cp>\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cvar>w\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>w\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cvar>r\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>r\u003C/var>\u003C/span>\u003C/p>\u003Cp>    third group: \u003Cspan class='formula rendered-math'>\u003Cvar>i\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>i\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fourth group: \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fifth group: \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>, \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>\u003C/p>\u003Cp>    sixth group: \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>    seventh group: \u003Cspan class='formula rendered-math'>\u003Cvar>o\u003C/var>\u003C/span>, \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>\u003C/p>\u003Cp>    eighth group: \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>\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'>\u003Cspan class='number'>6\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>12\u003C/span>\u003Cvar>w\u003C/var>\u003Cvar>w\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>r\u003C/var>\u003Cvar>i\u003C/var>\u003Cvar>i\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>t\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>e\u003C/var>\u003Cvar>h\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>a\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>f\u003C/var>\u003Cvar>k\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>s\u003C/var>\u003Cvar>d\u003C/var>\u003Cvar>y\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_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>\u003Ccenter>\u003Cp>Numerical \u003Ca href = \"#FACTOR_NOUN\">factors\u003C/a> will be multiplied.\u003C/p>\u003C/center>\u003Cp>The following are like factors:\u003C/p>\u003Cp>\u003C/p>\u003Cp>\u003C/p>\u003Cp>    first group: \u003Cspan class='formula rendered-math'>\u003Cvar>w\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>w\u003C/var>\u003C/span>\u003C/p>\u003Cp>    second group: \u003Cspan class='formula rendered-math'>\u003Cvar>r\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>r\u003C/var>\u003C/span>\u003C/p>\u003Cp>    third group: \u003Cspan class='formula rendered-math'>\u003Cvar>i\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>i\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fourth group: \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>t\u003C/var>\u003C/span>\u003C/p>\u003Cp>    fifth group: \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>e\u003C/var>\u003C/span>, \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>\u003C/p>\u003Cp>    sixth group: \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>    seventh group: \u003Cspan class='formula rendered-math'>\u003Cvar>o\u003C/var>\u003C/span>, \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>\u003C/p>\u003Cp>    eighth group: \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>\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'>\u003Cspan class='number'>72\u003C/span>\u003Cvar>w\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>\u003C/span>\u003C/sup>\u003Cvar>r\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>i\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>\u003C/span>\u003C/sup>\u003Cvar>t\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>\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 s4'>\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>h\u003C/var>\u003Cvar>a\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>\u003C/span>\u003C/sup>\u003Cvar>o\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>\u003Cspan class='binary-operator'>+\u003C/span>\u003Cspan class='number'>1\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>f\u003C/var>\u003Cvar>k\u003C/var>\u003Cvar>s\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>\u003C/span>\u003C/sup>\u003Cvar>d\u003C/var>\u003Cvar>y\u003C/var>\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'>\u003Cspan class='number'>72\u003C/span>\u003Cvar>w\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>r\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r1'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>i\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r2'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>t\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r3'>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>e\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r4'>\u003Cspan class='number'>4\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>h\u003C/var>\u003Cvar>a\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r5'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>o\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r6'>\u003Cspan class='number'>3\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>f\u003C/var>\u003Cvar>k\u003C/var>\u003Cvar>s\u003C/var>\u003Csup class='non-leaf'>\u003Cspan class='non-leaf r7'>\u003Cspan class='number'>2\u003C/span>\u003C/span>\u003C/sup>\u003Cvar>d\u003C/var>\u003Cvar>y\u003C/var>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: 72*{w}^{2}*{r}^{2}*{i}^{2}*{t}^{4}*{e}^{4}*h*{a}^{2}*{o}^{3}*f*k*{s}^{2}*d*y-->\n\u003C/div>\n \u003C/div> \u003C/div> ","72*{w}^{2}*{r}^{2}*{i}^{2}*{t}^{4}*{e}^{4}*h*{a}^{2}*{o}^{3}*f*k*{s}^{2}*d*y","write\\th eratioof6weeksto12days","writeth eratioof6weeksto12days",{"row_html":107,"answer":108,"solver_type":84,"expression_latex":109,"expression":110}," \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 s0'>\u003Cspan class='number'>3.4\u003C/span>\u003Cvar>c\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>s\u003C/var>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>13\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 = \"#TERM\">terms\u003C/a> are commonly written first.\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'>3.4\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>13\u003C/span>\u003Cvar>c\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>s\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>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 r0'>\u003Cspan class='number'>44.2\u003C/span>\u003Cvar>c\u003C/var>\u003Cvar>o\u003C/var>\u003Cvar>s\u003C/var>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: 44.2*c*o*s-->\n\u003C/div>\n \u003C/div> \u003C/div> ","44.2*c*o*s","3.4\\cos13","3.4cos 13",{"row_html":112,"answer":113,"solver_type":84,"expression_latex":114,"expression":114}," \u003Cdiv> \u003Ch3>Solution step by step\u003C/h3> \u003Cdiv class=\"steps-r\"> \u003C!-- STEPS-NUM: 2 -->\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>B\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf s0'>\u003Cspan class='number'>180\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>20.2\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='number'>53.1\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 = \"#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>B\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='number'>106.7\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: B=106.7-->\n\u003C/div>\n\u003Cbr clear='both' />\u003Cbr clear='both' />\u003Cbr clear='both' />\n \u003C/div> \u003C/div> ","B=106.7","B=180-20.2-53.1",{"row_html":116,"answer":117,"solver_type":84,"expression_latex":118,"expression":119}," \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>f\u003C/var>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²numberβ€²>5\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€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!-- 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 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'>\u003Cvar>f\u003C/var>\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='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>f\u003C/var>\u003Cvar>x\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cvar>f\u003C/var>\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='binary-operator'>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>5\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>\u003Cspan class='denominator'>\u003Cvar>f\u003C/var>\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'>\u003Cvar>f\u003C/var>\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 convert this \u003Ca href = \"#COMPLEX_FRACTION\">complex fraction\u003C/a> into a division problem by replacing the main fraction line with the division symbol:\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>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cvar>AΓ·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='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>5\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> and\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>B\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cvar>f\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'>\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='binary-operator'>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>5\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>\u003Cspan class='binary-operator'>÷\u003C/span>\u003Cvar>f\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 perform a division by multiplying the \u003Ca href = \"#DIVIDEND\">dividend\u003C/a> with the \u003Ca href = \"#RECIPROCAL\">reciprocal\u003C/a> of the \u003Ca href = \"#DIVISOR\">divisor\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>\u003Cspanclass=β€²fractionnonβˆ’leafβ€²>\u003Cspanclass=β€²numeratorβ€²>\u003Cvar>A\u003C/var>\u003C/span>\u003Cspanclass=β€²denominatorβ€²>\u003Cvar>B\u003C/var>\u003C/span>\u003Cspanstyle=β€²display:inlineβˆ’block;width:0β€²>\u003C/span>\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Cvar>Γ·\u003C/var>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²fractionnonβˆ’leafβ€²>\u003Cspanclass=β€²numeratorβ€²>\u003Cvar>C\u003C/var>\u003C/span>\u003Cspanclass=β€²denominatorβ€²>\u003Cvar>D\u003C/var>\u003C/span>\u003Cspanstyle=β€²display:inlineβˆ’block;width:0β€²>\u003C/span>\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>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²fractionnonβˆ’leafβ€²>\u003Cspanclass=β€²numeratorβ€²>\u003Cvar>A\u003C/var>\u003C/span>\u003Cspanclass=β€²denominatorβ€²>\u003Cvar>B\u003C/var>\u003C/span>\u003Cspanstyle=β€²display:inlineβˆ’block;width:0β€²>\u003C/span>\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²fractionnonβˆ’leafβ€²>\u003Cspanclass=β€²numeratorβ€²>\u003Cvar>D\u003C/var>\u003C/span>\u003Cspanclass=β€²denominatorβ€²>\u003Cvar>C\u003C/var>\u003C/span>\u003Cspanstyle=β€²display:inlineβˆ’block;width:0β€²>\u003C/span>\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\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'>5\u003C/span>\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 class='number'>2\u003C/span>\u003C/span>.\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>C\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\u003Cvar>f\u003C/var>\u003C/span> and\u003C/p>\u003Cp>    \u003Cspan class='formula rendered-math'>\u003Cvar>D\u003C/var>\u003C/span> is equal to \u003Cspan class='formula rendered-math'>\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'>\u003Cvar>x\u003C/var>\u003Cspan class='binary-operator'>=\u003C/span>\u003Cspan class='non-leaf r0'>\u003Cspan class='non-leaf s0'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²fractionnonβˆ’leafβ€²>\u003Cspanclass=β€²numeratorβ€²>\u003Cspanclass=β€²numberβ€²>5\u003C/span>\u003C/span>\u003Cspanclass=β€²denominatorβ€²>\u003Cspanclass=β€²numberβ€²>2\u003C/span>\u003C/span>\u003Cspanstyle=β€²display:inlineβˆ’block;width:0β€²>\u003C/span>\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\u003C/span>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspanclass=β€²nonβˆ’leafβ€²>\u003Cspanclass=β€²fractionnonβˆ’leafβ€²>\u003Cspanclass=β€²numeratorβ€²>\u003Cspanclass=β€²numberβ€²>1\u003C/span>\u003C/span>\u003Cspanclass=β€²denominatorβ€²>\u003Cvar>f\u003C/var>\u003C/span>\u003Cspanstyle=β€²display:inlineβˆ’block;width:0β€²>\u003C/span>\u003C/span>\u003C/span>\u003Cspanclass=β€²scaledparenβ€²>\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 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>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cvar>C\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cvar>D\u003C/var>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\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>\u003Cvar>D\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'>5\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>1\u003C/span>\u003C/span>,\u003C/p>\u003Cp>The factors in the new \u003Ca href = \"#DENOMINATOR\">denominator\u003C/a> are:\u003C/p>\u003Cp>\u003Cspan class='formula rendered-math'>\u003Cspan class='number'>2\u003C/span>\u003C/span>, \u003Cspan class='formula rendered-math'>\u003Cvar>f\u003C/var>\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='binary-operator'>−\u003C/span>\u003Cspan class='fraction non-leaf'>\u003Cspan class='numerator'>\u003Cspan class='number'>5\u003C/span>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>2\u003C/span>\u003Cvar>f\u003C/var>\u003C/span>\u003Cspan style='display:inline-block;width:0'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: x=-{5}/{2*f}-->\n\u003C/div>\n \u003C/div> \u003C/div> ","x=-{5}/{2*f}","f\\leftxright=-\\frac52","fx=-5/2",{"row_html":121,"answer":122,"solver_type":123,"expression_latex":124,"expression":124}," \u003Cdiv> \u003Ch3>Factor\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'>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003Cvar>f\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='non-leaf s1'>\u003Cspan class='number'>21\u003C/span>\u003C/span>\u003Cvar>h\u003C/var>\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'>3\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'>3\u003C/span>\u003C/span>.\u003C/p>\u003Cp>     Prime number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>7\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'>7\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>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'>3\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'>3\u003C/span>\u003C/span>.\u003C/p>\u003Cp>     Prime number \u003Cspan class='formula rendered-math'>\u003Cspan class='number'>7\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'>7\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 class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cvar>f\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003Cvar>h\u003C/var>\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003Cvar>f\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003Cvar>h\u003C/var>\u003C/span>\u003Cspan class='denominator'>\u003Cspan class='number'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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>\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>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\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'>3\u003C/span>\u003Cspan class='binary-operator'>·\u003C/span>\u003Cspan class='number'>7\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='non-leaf r0'>\u003Cvar>f\u003C/var>\u003C/span>\u003Cspan class='non-leaf r1'>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>h\u003C/var>\u003C/span>\u003C/span>\u003Cspan class='scaled paren'>\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 r0'>\u003Cspan class='number'>21\u003C/span>\u003Cspan class='non-leaf'>\u003Cspan class='scaled paren'>\u003C/span>\u003Cspan class='non-leaf'>\u003Cvar>f\u003C/var>\u003Cspan class='binary-operator'>−\u003C/span>\u003Cvar>h\u003C/var>\u003C/span>\u003Cspan class='scaled paren'>\u003C/span>\u003C/span>\u003C/span>\u003C/div>\u003C/div>\n\n\u003C!-- RESULT: 21*fβˆ’h-->\n\u003C/div>\n \u003C/div> \u003C/div> ","21*fβˆ’h","factor","21f-21h",{"data":126},[127,131,134,137,140,144,147,150],{"id":128,"h1":129,"slug":130},8,"Math Sequence Solver","math-sequence-solver",{"id":13,"h1":132,"slug":133},"Math Word Problem Solver App","math-word-problem-solver-app",{"id":22,"h1":135,"slug":136},"Math Story Problem Solver","math-story-problem-solver",{"id":16,"h1":138,"slug":139},"Best Math Problem Solver App","best-math-problem-solver-app",{"id":141,"h1":142,"slug":143},7,"Math Fill In The Blank 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