Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 160: 71

$(-\infty,5)$

Step 1. Rewrite the inequality as $\frac{x+3}{x-5}-1\le0$ or $\frac{8}{x-5}\le0$ Step 2. Identify the boundary point as $x=5$ Step 3. Use test points at $x=0,6$, the signs of the left side rational are $-,+$ Step 4. The inequality requires negative (left region, excluding $x=5$), thus the solution interval is $(-\infty,5)$