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: If
then
2. If we multiply or divide both sides by a positive number the inequality sign is unchanged i.e.
and
then
and
Example: If
then
3. If we multiply or divide both sides by a negative number, the inequality sign is reversed i.e. and
then
and
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