Answer
the interval $\left(-\infty, \dfrac{3}{2}\right)\cup[5,\infty)$
Work Step by Step
Using the properties of inequality, the given expression, $
-3\lt2(x-3)\le4
,$ simplifies to
\begin{array}{l}\require{cancel}
-3\lt2x-6\le4
\\\\
-3+6\lt2x-6+6\le4+6
\\\\
3\lt2x\le10
\\\\
\dfrac{3}{2}\lt\dfrac{2}{2}x\le\dfrac{10}{2}
\\\\
\dfrac{3}{2}\lt x\le5
.\end{array}
Hence, the solution set is $\text{
the interval $\left(-\infty, \dfrac{3}{2}\right)\cup[5,\infty)$
.}$
