**Inequalities – Definitions of Terms**

**Absolute Value: **The distance a number is from 0. If x is a positive real number, then its absolute value, |x|, is x. For example, if x is 3, then |x| = |3| = 3. If x is a negative real number, then |x| = -x. For example, if x is -3, then |x| = |-3| = -(-3) = 3. Notice that both 3 and -3 are the same distance, 3, from 0.

**Inequality: **A mathematical statement that two quantities are comparable but not necessarily equal. Usually, it includes an indication as to which quantity is greater or less. For example: x ≤ 3, says x can be 3, but it might be less than 3. As a second example, x < 3 says x is definitely less than 3. Inequalities are expressed using the following operators: <, >, ≤, ≥, ≠.

Inequalities are solved just as equations are, with one notable exception. In an inequality, if you multiply or divide both sides by the same *negative* number, then you reverse the direction of the inequality.