Section 2.5 Compound Inequalities 111 Student Check 5 Write a compound inequality that represents each situation and solve the inequality. Use a complete sentence to answer each question. a. Bryan is 6 ft tall. How much should he weigh to have a normal BMI? Use the formula in Example 5(a). b. Ameena is attempting to earn a C in her chemistry class. Her final grade is computed as follows: 60% (test average), 15% (quizzes), and 25% (final exam). Ameena has a test average of 62 and a quiz average of 78. What grades could she earn on her final to have a final grade between 70 and 79? Troubleshooting Common Errors Some common errors related to solving compound inequalities are shown. Objective 6 Examples A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 6a. Solve 5x - 5<-5 or -2x < 0. Incorrect Solution Correct Solution and Explanation 5x - 5<-5 or -2x < 0 5x < 0 or x 0 x < 0 The solution set numbers, or . 6b. Solve 5x - 5≤-5 or -2x ≤ 0. Incorrect Solution Correct Solution and Explanation 5x - 5≤-5 or -2x ≤ 0 ≤ 0 or ≥ 0 x ≤ 0 The solution set set, or . Objective 6 ▶ Troubleshoot common errors. Since neither inequality includes zero as a solution, the union can’t include zero. So, the solution set is (-∞, 0) ∪ (0, ∞). Since both inequalities include zero as a solution, the intersection will include zero. So, the solution set is {0}. 5 < 5 0 > is all real nu 5 ≤ 5x 0 x t is the empty s ANSWERS TO STUDENT CHECKS Student Check 1 a. 0 1 2 3 4 5 6 7 8 9 10 5, 6); 5xu5 ≤ x < 66 b. –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 (-∞, -4); 5xux<-46 c. Student Check 2 a. (-∞, 0 ∪ (4, ∞) b. (-∞, 3) c. (-∞, ∞) Student Check 3 a. -3, 2 –5 –4 –3 –2 –1 0 1 2 3 4 5 b. (5, ∞) 0 1 2 3 4 5 6 7 8 9 10 c. d. a- 7 9 , 1b 7 9 – –5 –4 –3 –2 –1 0 1 2 3 4 5
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