Answer
$(-\infty,1]\cup[3,\infty)$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$\Rightarrow 3x+2\leq5$ or $5x-7\geq8$.
Solve each inequality separately.
$\Rightarrow 3x+2\leq5$ or $5x-7\geq8$.
$\Rightarrow 3x\leq5-2$ or $5x\geq8+7$.
$\Rightarrow 3x\leq3$ or $5x\geq15$.
$\Rightarrow x\leq1$ or $x\geq3$.
First graph then take the union of the solution sets of the two inequalities.
The graph is shown in the image file.
We can write the compound inequality.
$x\leq1$ as $(-\infty,1]$ and $x\geq3$ as $[3,\infty)$
The union is
$(-\infty,1]\cup[3,\infty)$.
