190 Chapter 2 Linear Equations and Inequalities Solving a Linear Inequality Example 7 Solve the inequality and graph the solution set. Express the solution set in set- builder notation and in interval notation. Solution: 2 3 k Multiply both sides by 12 to clear fractions. (Because we multiplied by a positive number, the inequality sign is not reversed.) Apply the distributive property. Simplify. Subtract 8k from both sides. Subtract 2 from both sides. 12a 1 4 1 4 k k kb 1 6 2 1 4 2 3 k k 1 6b 12a2 12 1 a1 6 b 12122 3k 2 24 8k 12 1 a 1 4 2 3 1 6 kb 2 12 1 a2 3 3k 8k 2 24 8k 8k 11k 2 24 11k 2 2 24 2 11k 22 11k 11 22 11 k 2 kb Divide both sides by . Reverse the inequality sign. Set-builder notation: Interval notation: 32, 2 4 3 2 1 0 1 2 3 4 5k ƒ k 26 11 Skill Practice Solve the inequality and graph the solution set. Express the solution set in set-builder notation and in interval notation. 13. 1 5 t 7 1 2 t 2 Classroom Example: p. 195, Exercise 90 Skill Practice Solve the inequality and graph the solution set. Express the solution set in set-builder notation and in interval notation. 14. 3 5 2y 6 11 Answers 13. 14. 5t ƒ t 306; 30, ) 30 5. Inequalities of the Form a x b To solve a compound inequality of the form we can work with the inequality as a three-part inequality and isolate the variable, x, as demonstrated in Example 8. Solving a Compound Inequality of the Form a x b Solve the inequality and graph the solution set. Express the solution set in set-builder notation and in interval notation. 3 2x 1 6 7 Example 8 a 6 x 6 b Classroom Example: p. 195, Exercise 70 5y ƒ 1 y 6 86; 1, 8) ( 1 8
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