Answer
$[-\frac{5}{3}, 3)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{3(x+5/3)}{2(x-3)}\leq0$; the boundary points are $x=-5/3,3$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-5/3)...(-)...(3)...(+)...$
Thus the solutions are $-\frac{5}{3}\leq x\lt3$
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 $[-\frac{5}{3}, 3)$
