Answer
$(-\infty,3)\cup[10,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as
$\frac{2x+1}{x-3}-3=\frac{2x+1-3x+9}{x-3}=\frac{-x+10}{x-3}\leq0$
or
$\frac{x-10}{x-3}\geq0$
Thus the boundary points are $x=3,10$
Step 2. Using test points to examine the signs of the left side across the boundary points, we have
$...(+)...(3)...(-)...(10)...(+)...$
Thus the solutions are:
$(-\infty,3)\cup[10,\infty)$
Step 3. We can graph the above solution on a real number line as shown.
