Intermediate Algebra, Chapter 2, 2.6, Section 2.6, Problem 62

For compound inequality $-8x \leq -24$ or $-5x \geq 15$, decide whether intersection or union should be used. Then give the solution set in both interval and graph form.

We solve the inequality individually


$
\begin{equation}
\begin{aligned}

-8x \leq & -24 && \qquad \text{or} &&& -5x \geq & 15
\\
x \geq & 3 && \qquad \text{or} &&& x \leq & -3

\end{aligned}
\end{equation}
$


By graphing the two intervals, we have













By taking the union, we obtain every real number as a solution, since every real number satisfies at least one of the two inequalities. The set of all numbers is written in interval notation as $(- \infty, -3] \cup [3, \infty)$.