Answer
$(-\infty,\infty)$.
Work Step by Step
The given compound inequality is
$3x-2\gt-8$ or $2x+1\lt9$
Solve each inequality separately.
$\Rightarrow 3x-2\gt-8$ or $2x+1\lt9$
$\Rightarrow 3x-2+2\gt-8+2$ or $2x+1-1\lt9-1$
$\Rightarrow 3x\gt-6$ or $2x\lt8$
$\Rightarrow \frac{3x}{3}\gt\frac{-6}{3}$ or $\frac{2x}{2}\lt\frac{8}{2}$
$\Rightarrow x\gt-2$ or $x\lt4$
First graph then take the union of the two inequalities.
We can write the compound inequality.
$x\gt-2$ as $(-2,\infty)$ and $x\lt4$ as $(-\infty,4)$
The union is
$(-\infty,4)\cup(-2,\infty)=(-\infty,\infty)$.
The graph is shown below.
