Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 160: 60

$(-\infty,2)U[5,\infty)$

Step 1. Rewrite the inequality as $\frac{3}{x-2}-1\lt0$ or $\frac{5-x}{x-2}\lt0$ Step 2. Identify the boundary points as $x=2,5$ Step 3. Use test points at $x=0, 3,6$, the signs of the left side are $-, +, -$ Step 4. The inequality requires negative (outer regions excluding $x=2$), thus the solution intervals are $(-\infty,2)U[5,\infty)$