Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 160: 58

$(-2,4)$

Step 1. Rewrite the inequality as $\frac{6-x}{x+2}-1\gt0$ or $\frac{8-2x}{x+2}\gt0$ Step 2. Identify the boundary points as $x=-2, 4$ Step 3. Use test points at $x=-3, 0, 5$, the signs of the left side are $-, +, -$ Step 4. The inequality requires positive (middle region), thus the solution interval is $(-2,4)$