## Precalculus (6th Edition) Blitzer

$x\lt1$
Step 1. Rewrite the inequality as $\frac{x-2}{x-1}-1=\frac{x-2-x+1}{x-1}=\frac{-1}{x-1}\geq0$ or $\frac{1}{x-1}\leq0$ Step 2. We can find the solution set of the above as $x\lt1$ Step 3. We can graph the solution set on a real number line as shown in the figure.