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

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

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