Answer
$\left[ -\dfrac{7}{3},7 \right]$
Work Step by Step
Using properties of inequality, then,
\begin{array}{l}
-5\le \dfrac{-3x+1}{4}\le2\\\\
-5\cdot4\le \dfrac{-3x+1}{4}\cdot4\le2\cdot4\\\\
-20\le -3x+1\le8\\\\
-20-1\le -3x+1-1\le8-1\\\\
-21\le -3x\le7\\\\
7\ge x\ge-\dfrac{7}{3}\\\\
-\dfrac{7}{3}\le x\le7
.\end{array}
Hence, the solution set is $
\text{ the interval }
\left[ -\dfrac{7}{3},7 \right]
$.
