Solving inequalities

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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.

Example 1:

Solve the inequality 2(2c + 2) ≤ 5. Show the answer on a number line.


2(2c + 2) ≤ 5


Expand the bracket:

4c + 4 ≤ 5


Subtract 4 from both sides:

4c ≤ 1


Divide both sides by 4:

c ≤ 1/4


To show the answer on a number line, put a closed circle at $\frac{1}{4}$ and indicate the numbers that are less than $\frac{1}{4}$.

Solving inequalities