Answer
$(-3,6]$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$x-4\leq2$ and $3x+1\gt-8$.
Solve each inequality separately.
$\Rightarrow x-4\leq2$ and $3x+1\gt-8$.
$\Rightarrow x\leq2+4$ and $3x\gt-8-1$.
$\Rightarrow x\leq6$ and $3x\gt-9$.
$\Rightarrow x\leq6$ and $x\gt-3$.
First graph then take the intersection of the solution sets of the two inequalities..
The graph is shown in the image file.
We can write the compound inequality.
$x\leq6$ as $(-\infty,6]$ and $x\gt-3$ as $(-3,\infty)$
The intersection is
$(-\infty,6]\cap(-3,\infty)=(-3,6]$.
