2.2.3 Solving Absolute-Value Equations and Inequalities (continued) Example 4 Solving Absolute-Value Inequalities with Conjunctions Use a conjunction to rewrite the absolute-value inequality as a compound inequality when the absolute- value expression is less than (or less than or equal to) a constant. • If | x | < a , then x < a and x > − a . • If | x | ≤ a , then x ≤ a and x ≥ − a . Note an absolute-value inequality where the absolute-value expression is less than (or less than or equal to) a negative real number will have no real solutions. Recall that when both sides of an inequality are multiplied or divided by a negative number, the inequality symbol must be reversed.
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