Key Objectives • Write and graph compound inequalities. • Solve compound inequalities involving AND or OR. Key Terms • A compound inequality is a combination of two or more inequalities into one statement. Inequalities such as x ≤ 1 are called simple inequalities. When two simple inequalities are combined into one statement by the words AND or OR, the result is called a compound inequality. Example 1 Weather Application In Example 1, Prof. Burger writes a compound inequality and graphs its solutions. 3.2.3 Solving Compound Inequalities
Example 2 Solving Compound Inequalities Involving AND
The compound inequality A ≤ x ≤ B is a shorthand way of writing A ≤ x AND x ≤ B . The solution of an AND inequality is the intersection (overlapping region) of the solutions of each corresponding simple inequality. To solve an AND compound inequality, solve each simple inequality or isolate the variable as a three-part inequality.
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