Answer
$(5,\infty)$.
Work Step by Step
The given compound inequality is
$-2x\leq6$ and $-2x+3\lt-7$.
Solve each inequality separately.
First $-2x\leq6$.
Divide both sides by $-2$ and change the sense of the inequality.
$\Rightarrow \frac{-2x}{-2}\geq\frac{6}{-2}$
Simplify.
$\Rightarrow x\geq-3$
Second $-2x+3\lt-7$.
Subtract $3$ from both sides.
$\Rightarrow -2x+3-3\lt-7-3$
Simplify.
$\Rightarrow -2x\lt-10$
Divide both sides by $-2$ and change the sense of inequality.
$\Rightarrow \frac{-2x}{-2}\gt\frac{-10}{-2}$
Simplify.
$\Rightarrow x\gt5$
First graph and then take the intersection of the two inequality.
We can write the compound inequality.
$x\geq-3$ as $[-3,\infty)$ and $x\gt5$ as $(5,\infty)$
The intersection is
$[-3,\infty)\cap(5,\infty)=(5,\infty)$.
The combined graph is shown below.
