Section 2.5 Compound Inequalities 109 Now we find the union of the two solution sets. Inequality 1 x ≥ 9 9, ∞) 9 –8 –6 –4 –2 0 2 4 6 8 10 12 Inequality 2 x≤- 8 3 a-∞, - 8 3 d 8 3 – –8 –6 –4 –2 0 2 4 6 8 10 12 Union of two sets a-∞, - 8 3 d ∪ 9, ∞) 8 3 – 9 –8 –6 –4 –2 0 2 4 6 8 10 12 We can check by substituting values from the union of the inequalities and will find that these values make at least one of the inequalities true. So, the solution set is a-∞, - 8 3 d ∪ 9, ∞). 4c. 2x - 4>-8 or 7x - 5 < 2 7x - 5 + 5 < 2 + 5 7x < 7 x < 1 2x - 4 + 4>-8 + 4 Add 4 to each side. Simplify. Divide each side by 2. 2x>-4 x>-2 Now we find the union of the two solution sets. Inequality 1 Add 5 to each side. Simplify. Divide each side by 7. x>-2 (-2, ∞) –5 –4 –3 –2 –1 0 1 2 3 4 5 Inequality 2 x < 1 (-∞, 1) –5 –4 –3 –2 –1 0 1 2 3 4 5 Union of two sets (-∞, ∞) –5 –4 –3 –2 –1 0 1 2 3 4 5 We can check by substituting any number into the original inequality and find that it makes the compound inequality true. So, the solution set is all real numbers, , or (-∞, ∞). Student Check 4 Solve each compound inequality. Write each solution set in interval notation and graph the solution set. a. x - 1 > 4 or -2x>-10 b. 9 4 x - 5≥-3 or 6(x + 2) < 7 c. -4x - 9>-1 or 2 - 3x < 11 Applications Applications of compound inequalities arise when there are two conditions that define a situation. When both conditions must be satisfied, an “and” statement is used. When only one of the conditions must be satisfied, an “or” statement is used. Objective 5 ▶ Solve applications of compound inequalities.
hendricks_intermediate_algebra_1e_ch1_3
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