Answer
$(-\frac{22}{3},\frac{14}{3})$
Work Step by Step
Step 1. We can remove the absolute sign to get: $-3\lt\frac{1}{2}x+\frac{2}{3}\lt3$
Step 2. Multiply $6$ to the entire inequality to get $-18\lt 3x+4\lt18\longrightarrow -22\lt 3x\lt14\longrightarrow -\frac{22}{3}\lt x\lt\frac{14}{3}$ or in interval notation $(-\frac{22}{3},\frac{14}{3})$
