Answer
$\text{ the interval }
\left[ 1,\dfrac{17}{2} \right]
$
Work Step by Step
Using properties of inequality, then,
\begin{array}{l}
-4\le \dfrac{-2x+5}{3}\le1\\\\
-4\cdot3\le \dfrac{-2x+5}{3}\cdot3\le1\cdot3\\\\
-12\le -2x+5\le3\\\\
-12-5\le -2x+5-5\le3-5\\\\
-17\le -2x\le-2\\\\
\dfrac{17}{2}\ge x\ge1\\\\
1\le x\le\dfrac{17}{2}
.\end{array}
Hence, the solution set is $
\text{ the interval }
\left[ 1,\dfrac{17}{2} \right]
$.
