Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 46

$(-4,3)$

Step 1. Rewrite the inequality as $x^2+x-12\lt0$ Step 2. Factor the quadratic, we have $(x+4)(x-3)\lt0$ Step 3. The boundary points are $x=-4$ and $x=3$ Step 4. Use test points at $x=-5, 0$, 4, the signs of the quadratic are $+, -, +$ Step 5. The inequality requires negative, thus the solution interval (middle region) is $(-4,3)$