Answer
$\left\{x\ |\ -5.5 \lt x \lt 0.5 \right\}$ or $\left[-5.5,0.5\right]$
Work Step by Step
$-3 \lt \displaystyle \frac{2x-1}{4} \lt 0 \qquad$ ... multiply with 4
$-12 \lt 2x-1 \lt 0 \qquad$ ... add 1
$-11 \lt 2x \lt 1 $... divide with $2$
$-5.5 \lt x \lt 0.5$
Solution set: $\left\{x\ |\ -5.5 \lt x \lt 0.5 \right\}$ or $\left[-5.5,0.5\right]$