Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 160: 57

$(-\infty,-2)$

Step 1. Rewrite the inequality as $\frac{1-x}{x+2}+1\lt0$ or $\frac{3}{x+2}\lt0$ Step 2. Identify the boundary point as $x=-2$ Step 3. Use test points at $x=-3, 0$, the signs of the left side are $-, +$ Step 4. The inequality requires negative (left region), thus the solution interval is $(-\infty,-2)$