Answer
$\displaystyle \left\{x\ |\ -\frac{2}{3} \lt x \lt 2 \right\}$ or $\displaystyle \left(-\frac{2}{3},2\right)$
Work Step by Step
$0 \lt \displaystyle \frac{3x+2}{2} \lt 4 \qquad$ ... multiply with $2$
$0 \lt 3x+2 \lt 8 \qquad$ ... add $-2$
$-2 \lt 3x \lt 6 $... divide with $3$
$-\displaystyle \frac{2}{3} \lt x \lt 2$
Solution set: $\displaystyle \left\{x\ |\ -\frac{2}{3} \lt x \lt 2 \right\}$ or $\displaystyle \left(-\frac{2}{3},2\right)$
