Answer
$[-3,8]$
See graph.
Work Step by Step
Step 1. $x^2-5x\le24 \Longrightarrow x^2-5x-24\le0 \Longrightarrow (x+3)(x-8)\le0$
Step 2. Identify boundary points $x=-3,8$ and form intervals $(-\infty,-3],[-3,8],[8,\infty)$
Step 3. Choose test values for each interval $x=-4,0,9$ and test the inequality to get results $False,\ True,\ False$
Step 4. Write the solution $[-3,8]$
Step 5. See graph.
