Answer
$[0,\frac{5}{3}]$
Work Step by Step
Step 1. Rewrite the inequality as $x(3x-5)\leq0$; the boundary points are $x=0,\frac{5}{3}$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(0)...(-)...(\frac{5}{3})...(+)...$
Thus the solutions are $0\leq x\leq \frac{5}{3}$
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 $[0,\frac{5}{3}]$
