Answer
$$x \ge -4 \text{ or } x \le -8$$
Refer to the graph below.
Work Step by Step
Solve each inequality:
\begin{align*}
8x &\gt -32\\\\
\frac{8x}{8} &\gt \frac{-32}{8}\\\\
x &\ge -4
\end{align*}
$$\text{or}$$
\begin{align*}
-6x&\ge 48\\\
\frac{-6x}{-6} &\le \frac{48}{-6}& \text{(Dividing by a negative number changes the inequality symbol)}\\\\
x&\le -8
\end{align*}
Graph each inequality to obtain the one in the attached image above.
Since the compound inequality involves the conjunction $\text{OR}$, then the solutions to the inequality are the combined numbers of the two graphs.
