Intermediate Algebra (12th Edition)

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

Chapter 1 - Review Exercises: 71

Answer

$\left[ -3,-2 \right]$

Work Step by Step

Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the given inequality, $ |2x+5|\le1 ,$ is equivalent to \begin{array}{l}\require{cancel} -1\le 2x+5\le1 .\end{array} Using the properties of inequality, then \begin{array}{l}\require{cancel} -1-5\le 2x+5-5\le1-5 \\\\ -6\le 2x\le-4 \\\\ -\dfrac{6}{2}\le \dfrac{2x}{2}\le-\dfrac{4}{2} \\\\ -3\le x\le-2 .\end{array} Hence, the solution is the interval $ \left[ -3,-2 \right] .$
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