Answer
$(-\infty,1]$.
The graph of the solution set is shown below.
Work Step by Step
The given compound inequality is
$\Rightarrow 5x+3\leq18$ and $2x-7\leq-5$.
First
$\Rightarrow 5x+3\leq18$
Subtract $3$ from both sides.
$\Rightarrow 5x+3-3\leq18-3$
Simplify.
$\Rightarrow 5x\leq15$
Divide both sides by $5$.
$\Rightarrow \frac{5x}{5}\leq\frac{15}{5}$
Simplify.
$\Rightarrow x\leq3$
Second
$\Rightarrow 2x-7\leq-5$
Add $7$ to both sides.
$\Rightarrow 2x-7+7\leq-5+7$
Simplify.
$\Rightarrow 2x\leq2$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}\leq\frac{2}{2}$
Simplify.
$\Rightarrow x\leq1$
First graph then take the intersection of the solution sets of the two inequalities.
We can write the compound inequality.
$x\leq 1$ as $(-\infty,1]$ and $x\leq 3$ as $(-\infty,3]$
The intersection is
$(-\infty,1]\cap(-\infty,3]=(-\infty,1]$.
The graph is shown below.
