Answer
$ [-1,0]\cup[1,\infty)$.
Work Step by Step
Step 1. Rewrite the inequality $x^3-x\ge0 \Longrightarrow x(x+1)(x-1)\ge0$, identify boundary points as $x=-1,0,1$.
Step 2. Form intervals $(-\infty,-1],[-1,0],[0,1],[1,\infty)$.
Step 3. Choose test values for each 1interval $x=-2,-0.5,0.5,2$.
Step 4. Test the inequality to get results: $False,\ True,\ False,\ True$
Step 5. We have the solution $ [-1,0]\cup[1,\infty)$.
