Answer
$(-\infty,-6]\cup(-2,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as
$\frac{x-2}{x+2}-2\leq0$
which gives
$\frac{x-2-2x-4}{x+2}\leq0$, $\frac{-x-6}{x+2}\leq0$
and
$\frac{x+6}{x+2}\geq0$
Thus the boundary points are $x=-6,-2$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-6)...(-)...(-2)...(+)...$
Thus the solutions are $x\leq-6$ plus $x\gt-2$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $(-\infty,-6]\cup(-2,\infty)$
