Answer
$ [-3,8]$
See graph.
Work Step by Step
Step 1. Factor the inequality $x^2-5x-24\le0 \longrightarrow (x+3)(x-8)\le0$
Step 2. Identify the boundary points $x=-3,8$ and the intervals $(-\infty,-3],[-3,8)],[8,\infty)$
Step 3. Choose test values $x=-4,0,9$ and evaluate the inequality to get $False,\ True,\ False$
Step 4. Thus the solution interval is $ [-3,8]$
Step 5. See graph.
