Answer
$\text{the interval }
\left( 5,\infty \right]
$
Work Step by Step
Using the properties of inequality, the solution to the given inequality, $
-2x\le6 \text{ and } -2x+3\lt-7
,$ is
\begin{array}{l}\require{cancel}
x\ge\dfrac{6}{-2}
\\\\
x\ge-3
\\\\\text{ AND }\\\\
-2x+3\lt-7
\\\\
-2x\lt-7-3
\\\\
-2x\lt-10
\\\\
x\gt\dfrac{-10}{-2}
\\\\
x\gt5
.\end{array}
Combining the two inequalities, in interval notation, the solution is $
\text{the interval }
\left( 5,\infty \right]
.$