90 Chapter 1 Linear Equations and Inequalities in One Variable Solving an Inequality of the Form a < x < b Example 7 Solve the inequality. Solution: 4 6 3x 5 10 4 6 3x 5 10 4 6 3x 5 3x 5 10 and Set up the intersection of two inequalities. 9 6 3x 3x 5 and Solve each inequality. and and Take the intersection of the solution sets. 3 6 x 5 3 3x 3 x 5 3 5 3 ) 54 3 2 1 0 1 2 3 4 5 53 5x 0 3 53 6 x 6, 4. 9 3 6 3x 3 3 6 x The solution is or equivalently in interval notation, Skill Practice Solve the inequality. 11. 6 2x 5 6 1 13, 53 To solve an inequality of the form a < x < b, we can also work with the inequality as a “three-part” inequality and isolate x.This is demonstrated in Example 8. Answers 11. 5x 0 35t 0 , 32 66; 1 12. 20 6 t 6 20, 62 12 12 x 6 36; Solving an Inequality of the Form a < x < b Isolate the variable in the middle part. Multiply all three parts by 3.Remember to reverse the inequality signs. Solve the inequality. Solution: 3122 3ap 2 3 6 p 2 3 6 2 p 2 2 3 2 4 p 5 54 3 2 1 0 1 2 3 4 5 Simplify. Add 2 to all three parts to isolate p. 5p 04 p 56 The solution is ,or equivalently in interval notation 4, 5. Skill Practice Solve the inequality. 12. 8 7 t 4 2 7 5 b 3112 2 p 2 3 1 2 p 2 3 1 Example 8
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