Answer
$r\lt-20 $ or $r\geq -5$
The graph is shown below.

Work Step by Step
The given inequality is
$\Rightarrow \frac{r}{4}\lt -5$ or $-2r-7 \leq 3$
Solve the first inequality.
$\Rightarrow \frac{r}{4}\lt -5$
Multiply each side by $4$.
$\Rightarrow 4(\frac{r}{4})\lt 4(-5)$
Simplify.
$\Rightarrow r\lt -20$
Solve the second inequality.
$\Rightarrow -2r-7 \leq 3$
Add $7$ to each side.
$\Rightarrow -2r-7+7 \leq 3+7$
Simplify.
$\Rightarrow -2r\leq 10$
Divide each side by $-2$. Reverse the inequality symbol.
$\Rightarrow \frac{-2r}{-2}\geq \frac{10}{-2}$
Simplify.
$\Rightarrow r\geq -5$
Hence, the solution is $r\lt-20 $ or $r\geq -5$.