#### Answer

$\left[ -\dfrac{9}{2},\dfrac{15}{2} \right]$

#### Work Step by Step

Using the properties of inequality, the given inequality, $
-6\le\dfrac{3}{2}-x\le6
,$ simplifies to
\begin{array}{l}\require{cancel}
2(-6)\le2\left( \dfrac{3}{2}-x \right)\le2(6)
\\\\
-12\le3-2x\le12
\\\\
-12-3\le3-3-2x\le12-3
\\\\
-15\le-2x\le9
\\\\
\dfrac{-15}{-2}\ge\dfrac{-2x}{-2}\ge\dfrac{9}{-2}
\\\\
\dfrac{15}{2}\ge x\ge-\dfrac{9}{2}
\\\\
-\dfrac{9}{2}\le x\le\dfrac{15}{2}
.\end{array}
Hence, the solution is $
\left[ -\dfrac{9}{2},\dfrac{15}{2} \right]
.$