Answer
$(-\frac{3}{2},-\frac{7}{6})$
See graph.
Work Step by Step
Step 1. Remove the absolute value sign and transform the original inequality:
$|3x+4|\lt\frac{1}{2} \Longrightarrow -\frac{1}{2}\lt 3x+4 \lt\frac{1}{2} \Longrightarrow -1\lt 6x+8\lt 1 \Longrightarrow -9\lt 6x\lt -7 \Longrightarrow -\frac{3}{2}\lt x\lt-\frac{7}{6}$ or $(-\frac{3}{2},-\frac{7}{6})$
Step 2. See graph.
