Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Review Exercises: 70


$\left[ -1,13 \right]$

Work Step by Step

Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the given inequality, $ |-x+6|\le7 ,$ is equivalent to \begin{array}{l}\require{cancel} -7\le -x+6 \le7 .\end{array} Using the properties of inequality, then \begin{array}{l}\require{cancel} -7-6\le -x+6-6 \le7-6 \\\\ -13\le -x \le1 \\\\ 13\ge x \ge-1 \\\\ -1\le x \le13 .\end{array} Hence, the solution is the interval $ \left[ -1,13 \right] .$
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