Answer
$\left[ -\dfrac{1}{3}, 3 \right]$
Work Step by Step
Using the properties of inequality, the given inequality, $
-2\le 3x-1\le 8
,$ simplifies to
\begin{array}{l}\require{cancel}
-2+1\le 3x-1+1\le 8+1
\\\\
-1\le 3x\le 9
\\\\
-\dfrac{1}{3}\le x\le \dfrac{9}{3}
\\\\
-\dfrac{1}{3}\le x\le 3
.\end{array}
Hence, the solution is the interval $
\left[ -\dfrac{1}{3}, 3 \right]
.$
