Answer
$(-\infty,-6)$.
Work Step by Step
The two given inequalities form a compound inequality:
$2x+5\leq11$ and $-3x\gt18$.
Solve each inequality separately.
$\Rightarrow 2x+5-5\leq11-5$ and $\frac{-3x}{-3}\lt\frac{18}{-3}$.
$\Rightarrow 2x\leq6$ and $x\lt-6$.
$\Rightarrow \frac{2x}{2}\leq\frac{6}{2}$ and $x\lt-6$.
$\Rightarrow x\leq3$ and $x\lt-6$.
First graph the solution set of each inequality, then take the intersection of the two solution sets.
We can write the solution sets:
$x\leq3$ 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.
