174 Chapter 2 Linear Equations and Inequalities Answer 12. 5. Inequalities of the Form a < x < b To solve a compound inequality of the form a 6 x 6 b 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 Example 8 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 Solution: To solve the compound inequality 3 2x 1 6 7 isolate the variable x in the middle. The operations performed on the middle portion of the inequality must also be performed on the left-hand side and right-hand side. Subtract 1 from all three parts of the inequality. Simplify. Divide by 2 in all three parts of the inequality. ( 3 2x 1 6 7 3 1 2x 1 1 6 7 1 4 2x 6 6 6 2 5x ƒ 2 x 636 4 2 2x 2 6 2 x 6 3 Set-builder notation: Interval notation: 32, 32 Skill Practice Solve the inequality and graph the solution set. Express the solution set in set-builder notation and in interval notation. 12. 3 5 2y 6 11 6 5 4 3 2 1 0 1 2 3 4 5 6 6. Applications of Linear Inequalities Table 2-2 provides several commonly used translations to express inequalities. 5y ƒ 1 y 6 86; 1, 8) ( 8 1 Table 2-2 English Phrase Mathematical Inequality a is less than b a 6 b a is greater than b a 7 b a exceeds b a is less than or equal to b a is at most b a b a is no more than b a is greater than or equal to b a is at least b a b a is no less than b
miller_beginning_intermediate_algebra_4e_ch1_3
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