Answer
$(-\infty,-\frac{4}{3})\cup[2,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{2(x-2)}{3(x+4/3)}\geq0$; the boundary points are $x=-4/3,2$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-4/3)...(-)...(2)...(+)...$
Thus the solutions are $x\lt-\frac{4}{3}$ or $x\geq2$
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 $(-\infty,-\frac{4}{3})\cup[2,\infty)$
