Answer
$ (4,\infty)$
Work Step by Step
Step 1. Rewrite the inequality $\frac{x+2}{x-4}-1\ge0$ as $\frac{6}{x-4}\ge0$. Identify boundary points (zeros and asymptotes) as $x=4$ which divide the x-axis into two intervals $(-\infty,4),(4,\infty)$
Step 2. Choose test values in each interval $x=0,5$ and test the inequality to get $ False,\ True$
Step 3. Thus the solution interval is $ (4,\infty)$
