Answer
$\left( -3,\dfrac{7}{2} \right)$
Work Step by Step
Using the properties of inequality, the given inequality, $
-4\lt3-2x\lt9
,$ simplifies to
\begin{array}{l}\require{cancel}
-4-3\lt3-3-2x\lt9-3
\\\\
-7\lt -2x\lt6
\\\\
\dfrac{-7}{-2}\gt \dfrac{-2x}{-2}\gt\dfrac{6}{-2}
\\\\
\dfrac{7}{2}\gt x\gt-3
\\\\
-3\lt x\lt\dfrac{7}{2}
.\end{array}
Hence, the solution is the interval $
\left( -3,\dfrac{7}{2} \right)
.$