4. Solving Compound Inequalities: Or In Examples 9 and 10, we solve compound inequalities that involve inequalities joined by the word or. In such a case, the solution to the compound inequality is the union of the solution sets of the individual inequalities. Answer 13. 5t 0 t 2 or t 7 36; 1, 24 ´ 13, 2 Solving a Compound Inequality: Or Step 1 Solve and graph each inequality separately. Step 2 If the inequalities are joined by the word or, find the union of the two solution sets. Step 3 Express the solution set in interval notation or in set-builder notation. Solving a Compound Inequality: Or Example 9 Solve the compound inequality. 3y 5 7 4 or 4 y 6 Solution: 3y 5 7 4 4 y 6 or or Solve each inequality separately. 3y 7 9 y 2 y 1 2 1 or Reverse the inequality signs. 3y 3 6 9 3 y 6 3 or y 2 5y 0 y 6 36 ( 5y 0 y 26 Take the union of the solution sets: 5y 0 y 6 3 or y 26 6 5 4 3 2 1 0 1 2 3 4 5 6 6 5 4 3 2 1 0 1 2 3 4 5 6 6 5 4 3 2 1 0 1 2 3 4 5 6 5y 0 y 6 3 or y 26 ( The solution is or, equivalently in interval notation, 1, 32 ´ 32, 2. Skill Practice Solve the compound inequality. 13. 10t 8 12 or 3t 6 7 3 Section 1.5 Compound Inequalities 91
miller_intermediate_algebra_4e_ch1_3
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