Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 44

$(-4,-2)$

Step 1. Rewrite the inequality as $x^2+6x+8\lt0$ Step 2. Factor the quadratic, we have $(x+4)(x+2)\lt0$ Step 3. The boundary points are $x=-4$ and $x=-2$ Step 4. Use test points at $x=-5, -3, 0$, the signs of the quadratic are $+, -, +$ Step 5. The inequality requires negative, thus the solution interval (middle region) is $(-4,-2)$