College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.6 - Equations and Inequalities Involving Absolute Value - 1.6 Assess Your Understanding: 52

Answer

The solution set is {$x|x\geq-6 $ and $x\leq6$}.

Work Step by Step

$|-x|-|4|\leq2$ Simplify $|-x|-4\leq2$ Isolate the absolute value. $|-x|-4+4\leq2+4$ Add 4 both sides. $|-x|\leq6$ Solve absolute value $-6\leq-x\leq6$ $\frac{-6}{-1}\geq\frac{-x}{-1}\geq\frac{6}{-1}$Divide each term by -1 and reverse the inequality symbols. $6\geq{x}\geq-6$ $x\geq-6 $ and $x\leq6$ The solution set is {$x| x\geq-6 $ and $x\leq6$}.
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