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

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

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.