Answer
$(-\infty, -7)\cup(3,\infty)$
Work Step by Step
Step 1. Factor the inequality to get $(x+7)(x-3)\gt0$
Step 2. Identify the boundary points $x=-7, 3$ and separate the number line into three intervals $(-\infty, -7)$, $(-7,3)$ and $(3,\infty)$
Step 3. Use test points $x=-8,0,4$ to get the signs of the left side of the inequality as $+,-,+$
Step 4. Based on the signs, we have the solution as $(-\infty, -7)\cup(3,\infty)$
