Answer
$(-\infty,-3]\cup(-2,\infty)$
Work Step by Step
Step 1. Rewriting the inequality as $\frac{x+3}{x+2}\geq0$, the boundary points are $x=-3,-2$
Step 2. Using the test points to examine signs across the boundary points, we have
$...(+)...(-3)...(-)...(-2)...(+)...$
Thus the solutions are $x\leq-3$ or $x\gt-2$
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 $(-\infty,-3]\cup(-2,\infty)$
