Intermediate Algebra, Chapter 2, 2.6, Section 2.6, Problem 60

For compound inequality $2x - 6 \leq -18$ and $2x \geq -18$, 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}

2x - 6 \leq & -18 && \qquad \text{and} &&& 2x \geq & -18
\\
2x \leq & -12
\\
x \leq & -6 && \qquad \text{and} &&& x \geq & -9

\end{aligned}
\end{equation}
$


By graphing the two intervals, we have













We can see from the graph on each set that it intersects on the interval $[-9,-6]$.