Inequalities are mathematical expressions with unequal values on both sides. Unlike equations, here, we compare two values.
A solution to an inequality is a value that makes the inequality true. Inequality can have more than one solution.
The methodology for solving inequalities is the same as for equations – our goal is to have x (the variable) stand to the left of the inequality sign.
When the unknown in inequality has a negative coefficient, we should use an inverse operation.
Solve the inequality 2(2c + 2) ≤ 5. Show the answer on a number line.
2(2c + 2) ≤ 5
Step1:
Expand the bracket:
4c + 4 ≤ 5
Step2:
Subtract 4 from both sides:
4c ≤ 1
Step3:
Divide both sides by 4:
c ≤ 1/4
Step4:
To show the answer on a number line, put a closed circle at $\frac{1}{4}$ and indicate the numbers that are less than $\frac{1}{4}$.