Answer
$(-\infty,-1)U(8,\infty)$ or $\{x|x\lt-1\ or\ x\gt8\}$.
Work Step by Step
Step 1. $x(x-7)\gt8 \longrightarrow x^2-7x-8\gt0 \longrightarrow (x+1)(x-8)\gt0$.
Step 2. Identify boundary points $x=-1,8$ and form intervals $(-\infty,-1),(-1,8),(8,\infty)$.
Step 3. Choose test values $x=-2,0,9$ to test the inequality and get results $True,\ False,\ True$.
Step 4. Thus we have the solution $(-\infty,-1)U(8,\infty)$ or $\{x|x\lt-1\ or\ x\gt8\}$.
