2.2.3 Solving Absolute-Value Equations and Inequalities Key Objectives • Solve compound inequalities. • Write and solve absolute-value equations and inequalities. • Solve and graph absolute-value inequalities with disjunctions and conjunctions. Key Terms • A compound inequality is a combination of two or more inequalities into one statement linked by and or or . • A disjunction is a compound inequality that uses the word or . • A conjunction is a compound inequality that uses the word and . • The absolute value of a number x , written | x |, is the distance from x to 0 on a number line. Example 1 Solving Compound Inequalities A disjunction is true if and only if at least one of its parts is true. A conjunction is true if and only if all of its parts are true. Conjunctions can be written as a single statement. For example, the conjunction x ≥ − 3 and x < 2 can be written as the single statement − 3 ≤ x < 2.
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