In order to solve inequalities, we have to simplify them. In simplifying inequalities, we have to observe four rules.

1. If we add or subtract the same number to both sides of an inequality, the inequality

sign is maintained, i.e.and

Example: Ifthen

2. If we multiply or divide both sides by a positive number the inequality sign is unchanged i.e. andthenand

Example: Ifthen

3. If we multiply or divide both sides by a negative number, the inequality sign is reversed i.e. andthenand

Example: Ifthen

4. If both sides of an inequality are positive we can square both sides, maintaining the inequality sign, i.e.

Example:so

Example in the use of the rules. Solve

Use rule 1 to subtract 4 from both sides, obtaining

Use rule3 to divide by -2, obtaining