College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.6 - Equations and Inequalities Involving Absolute Value - 1.6 Assess Your Understanding - Page 133: 61


$-\frac{9}{4}\lt x\lt \frac{3}{4}$

Work Step by Step

We simplify as follows: $|\frac{2x+3}{3}-\frac{1}{2}|\lt1$ $-1\lt\frac{2x+3}{3}-\frac{1}{2}\lt1$ $-\frac{1}{2}\lt\frac{2x+3}{3}\lt\frac{3}{2}$ $-\frac{3}{2}\lt2x+3\lt\frac{9}{2}$ $-\frac{9}{2}\lt2x\lt\frac{3}{2}$ $-\frac{9}{4}\lt x\lt\frac{3}{4}$
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