Intermediate Algebra, Chapter 2, 2.6, Section 2.6, Problem 46

For compound inequality $3x + 2 \leq -7$ or $-2x + 1 \leq 9$, give the solution set in both interval and graph form.

Solve each inequality individually


$
\begin{equation}
\begin{aligned}

3x + 2 \leq & -7 \qquad \text{or} &&& -2x + 1 \leq & 9
\\
3x \leq & -9 \qquad \phantom{or} &&& -2x \leq & 8
\\
x \leq & -3 \qquad \text{or} &&& x \geq & -4

\end{aligned}
\end{equation}
$


The graphs of the two inequalities are













By taking the union, we obtain the interval $(- \infty, \infty)$