Answer
$(-\infty,8]$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$\Rightarrow 16-3x\geq-8$ or $13-x\gt4x+3$.
Solve each inequality separately.
$\Rightarrow 16-3x\geq-8$ or $13-x\gt4x+3$.
$\Rightarrow 16\geq-8+3x$ or $13\gt4x+3+x$.
$\Rightarrow 16+8\geq3x$ or $13-3\gt5x$.
$\Rightarrow 24\geq3x$ or $10\gt5x$.
$\Rightarrow 8\geq x$ or $2\gt x$.
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.
$8\geq x$ as $(-\infty,8]$ and $2\gt x$ as $(-\infty,2)$
The union is
$(-\infty,8]\cup(-\infty,2)=(-\infty,8]$.
