Answer
$\left[ -10,2 \right]$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property and the properties of inequality, the solution to the given inequality, $
-3\le\dfrac{1}{2}x+2\le3
,$ is
\begin{array}{l}\require{cancel}
-3\le\dfrac{1}{2}x+2\le3
\\\\
2(-3)\le2\left( \dfrac{1}{2}x+2 \right)\le2(3)
\\\\
-6\le x+4\le6
\\\\
-6-4\le x+4-4\le6-4
\\\\
-10\le x\le2
.\end{array}
Hence, the solution set is the interval $
\left[ -10,2 \right]
.$
