Answer
$(-\infty,4)\cup[\frac{23}{4},\infty)$
Work Step by Step
Step 1. Rewrite the given inequality as
$\frac{x+3}{x-4}-5=\frac{x+3-5x+20}{x-4}=\frac{-4x+23}{x-4}\leq0$ or $\frac{4x-23}{x-4}\geq0$
we can identify the boundary points as $x=4,\frac{23}{4}$
Step 2. Using test points to examine the signs of the left side across the boundary points, we have
$...(+)...(4)...(-)...(\frac{23}{4})...(+)...$
Thus the solutions are $(-\infty,4)\cup[\frac{23}{4},\infty)$
Step 3. We can graph the solution on a real number line as shown in the figure.
