Answer
$(-\infty,-3]\cup[1,\infty)$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$\Rightarrow 2x-5\leq-11$ or $5x+1\geq6$.
Solve each inequality separately.
$\Rightarrow 2x-5\leq-11$ or $5x+1\geq6$.
$\Rightarrow 2x\leq-11+5$ or $5x\geq6-1$.
$\Rightarrow 2x\leq-6$ or $5x\geq5$.
$\Rightarrow x\leq-3$ or $x\geq1$.
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.
$x\leq-3$ as $(-\infty,-3]$ and $x\geq1$ as $[1,\infty)$
The union is
$(-\infty,-3]\cup[1,\infty)$.
