Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 160: 65

$(-2,\infty)$

Step 1. Rewrite the inequality as $\frac{7}{x+2}-\frac{1}{x+2}\ge0$ or $\frac{6}{x+2}\ge0$ 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 positive (right regions, excluding $x=-2$), thus the solution intervals are $(-2,\infty)$