Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 59

Answer

$ (\frac{17}{6}, \frac{19}{6})$ See graph.

Work Step by Step

Step 1. $|(3x-2)-7|\lt \frac{1}{2}$ or $|3x-9|\lt \frac{1}{2}$ can be separated into $-\frac{1}{2}\lt 3x-9\lt \frac{1}{2}$ which lead to $\frac{17}{6}\lt x\lt \frac{19}{6}$, thus we have the solution $ (\frac{17}{6}, \frac{19}{6})$ Step 2. See graph.
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