2.2.3 Solving Absolute-Value Equations and Inequalities (continued) Example 3 Solving Absolute-Value Inequalities with Disjunctions Solve absolute-value inequalities using the same methods that are used to solve absolute-value equations. 1. Isolate the absolute-value expression, if necessary. 2. Rewrite the absolute-value inequality as a compound inequality. 3. Solve each part of the compound inequality. For an absolute-value expression that is greater than (or greater than or equal to) a constant, use a disjunction to rewrite the absolute-value inequality as a compound inequality. • If | x | > a , then x > a or x < − a . • If | x | ≥ a , then x ≥ a or x ≤ − a . Note that all real numbers will be solutions to the inequality when the absolute-value expression is greater than (or greater than or equal to) a negative real number.
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