Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 87


$\left( -6.001,-5.999 \right)$

Work Step by Step

For any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$. (The symbol $\lt$ may be replaced with $\le$.) Using the concept above, the solutions to the given inequality, $ \left| x+6 \right|\lt0.001 ,$ is \begin{array}{l}\require{cancel} -0.001\lt x+6\lt0.001 \\\\ -0.001-6\lt x\lt0.001-6 \\\\ -6.001\lt x\lt-5.999 .\end{array} In interval notation, the solution set is $ \left( -6.001,-5.999 \right) .$
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