Answer
$(-\infty,-3]\cup[0,3]$.
Work Step by Step
Step 1. Rewrite the inequality $x^3-9x\le0 \Longrightarrow x(x+3)(x-3)\le0$, identify boundary points as $x=-3,0,3$.
Step 2. Form intervals $(-\infty,-3],[-3,0],[0,3],[3,\infty)$.
Step 3. Choose test values for each interval $x=-4,-1,1,4$.
Step 4. Test the inequality to get results: $True,\ False,\ True,\ False$
Step 5. We have the solution $(-\infty,-3]\cup[0,3]$.
