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: 81


$\left( -2,\dfrac{2}{3} \right)$

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, $ |3x+2|\lt4 ,$ is \begin{array}{l}\require{cancel} -4\lt3x+2\lt4 \\\\ -4-2\lt3x\lt4-2 \\\\ -6\lt3x\lt2 \\\\ -\dfrac{6}{3}\lt x\lt\dfrac{2}{3} \\\\ -2\lt x\lt\dfrac{2}{3} .\end{array} In interval notation, the solution set is $ \left( -2,\dfrac{2}{3} \right) .$
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