Answer
$(-4,-2]$.
Work Step by Step
The given compound inequality is
$5-2x\geq9$ and $5x+3\gt-17$
Solve each inequality separately.
$\Rightarrow 5-2x\geq9$ and $5x+3\gt-17$
$\Rightarrow 5-2x-5\geq9-5$ and $5x+3-3\gt-17-3$
$\Rightarrow -2x\geq4$ and $5x\gt-20$
$\Rightarrow \frac{-2x}{-2}\leq\frac{4}{-2}$ and $\frac{5x}{5}\gt\frac{-20}{5}$
$\Rightarrow x\leq-2$ and $x\gt-4$
First graph then take the intersection of the two inequality.
We can write the compound inequality.
$x\leq-2$ as $(-\infty,-2]$ and $x\gt-4$ as $(-4,\infty)$
The intersection is
$(-\infty,-2]\cap(-4,\infty)=(-4,-2]$.
The graph is shown below.
