Answer
$x\lt1$
Work Step by Step
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.
