Answer
$(-\infty,-6)$.
The graph of the solution set is shown below.
Work Step by Step
The given compound inequality is
$2x+5\leq11$ and $-3x\gt18$.
Solve each inequality separately.
First $2x+5\leq11$.
Subtract $5$ from both sides.
$\Rightarrow 2x+5-5\leq11-5$
Simplify.
$\Rightarrow 2x\leq6$
Divide both sides $2$.
$\Rightarrow \frac{2x}{2}\leq\frac{6}{2}$
Simplify.
$\Rightarrow x\leq3$
Second $-3x\gt18$.
Divide both sides $-3$ and change the sense of inequality.
$\Rightarrow \frac{-3x}{-3}\lt\frac{18}{-3}$
Simplify.
$\Rightarrow x\lt-6$
First graph then take the intersection of the two inequalities.
We can write the compound inequality.
$x\leq3$ as $(-\infty,3]$ and $x\lt-6$ as $(-\infty,-6)$
The intersection is
$(-\infty,3]\cap(-\infty,-6)=(-\infty,-6)$.
The combined graph is shown below.
