Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 3 - Cumulative Review: 36

Answer

$[-2,18]$

Work Step by Step

We are given that $|-x+8|-2\leq8$. Add 2 to both sides. $|-x+8|\leq10$ Therefore, $-x+8\leq10$ and $-x+8\geq-10$. We can solve both equations to find solutions. For $-x+8\leq10$, subtract 8 from both sides. $-x\leq2$ Divide both sides by -1 (which will reverse the inequality sign). $x\geq-2$ For $-x+8\geq-10$, subtract 8 from both sides. $-x\geq-18$ Divide both sides by -1 (which will reverse the inequality sign). $x\leq18$ Therefore, the solution set consists of all values of x that are greater than or equal to -2 and less than or equal to 18.
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