Answer
$ (4,\infty)$.
Work Step by Step
Step 1. For $\frac{x+2}{x-4}-1\ge0\Longrightarrow \frac{6}{x-4}\ge0$, identify boundary points as $x=4$.
Step 2. Form intervals $(-\infty,4),(4,\infty)$.
Step 3. Choose test values for each interval $x=0,5$.
Step 4. Test the inequality to get results: $False,\ True$
Step 5. We have the solution $ (4,\infty)$.
