Answer
$(-4,-3)$ or $\{x|-4\lt x\lt -3\}$.
Work Step by Step
Step 1. $x^2+7x\lt-12 \longrightarrow x^2+7x+12\lt0 \longrightarrow (x+4)(x+3)\lt0$.
Step 2. Identify boundary points $x=-4,-3$ and form intervals $(-\infty,-4),(-4,-3),(-3,\infty)$.
Step 3. Choose test values $x=-5,-3.5,0$ to test the inequality and get results $False,\ True,\ False$.
Step 4. Thus we have the solution $(-4,-3)$ or $\{x|-4\lt x\lt -3\}$.
