Answer
$ [-8,-2) $.
Work Step by Step
Step 1. For $\frac{x-4}{2x+4}-1\ge0\Longrightarrow \frac{-x-8}{2x+4}\ge0$, identify boundary points as $x=-8,-2$.
Step 2. Form intervals $(-\infty,-8],[-8,-2),(-2,\infty)$.
Step 3. Choose test values for each interval $x=-9,-3,0$.
Step 4. Test the inequality to get results: $False,\ True,\ False $
Step 5. We have the solution $ [-8,-2) $.
