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.