88 Chapter 1 Linear Equations and Inequalities in One Variable As you work through the examples in this section, remember that multiplying or dividing an inequality by a negative factor reverses the direction of the inequality sign. Solving a Compound Inequality: And Solve the compound inequality. and Solution: 2x 6 6 x 5 7 and Solve each inequality separately. and Reverse the first inequality sign. x 2 x 7 3 and x 2 5x 0 x 7 36 5x 0 x 26 Take the intersection of the solution sets: 5x 0 3 6 x 26 ( 6 54 3 2 1 0 1 2 3 4 5 6 The solution is ,or equivalently in interval notation, Skill Practice Solve the compound inequality. 8. 5x2 8 and4x 7 24 Solving a Compound Inequality: And Solve the compound inequality. 4.4a 3.1 6 12.3 and 2.8a 9.1 6 6.3 Solution: 4.4a 3.1 6 12.3 2.8a 9.1 6 6.3 and and Solve each inequality separately. 4.4a 6 15.4 2.8a 6 15.4 and Reverse the second inequality sign. 2.8a 2.8 7 15.4 2.8 4.4a 4.4 6 15.4 4.4 Example 5 15x 3, 24. 0 3 6 x 26 2x 2 7 6 2 2x 6 6 x 5 7 Example 4 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 Answer 8. 5x 02 x 6 66; 32, 62 a 6 3.5 and a 7 5.5 5a 0 a 6 3.56 5a 0 a 7 5.56 The intersection of the solution sets is the empty set: { } ( 6 5 4 3 2 1 0 1 2 3 4 5 6 ( 6 54 3 2 1 0 1 2 3 4 5 6 6 54 3 2 1 0 1 2 3 4 5 6
miller_intermediate_algebra_4e_ch1_3
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