Answer
$(-\infty,-4]\cup[\frac{1}{2},\infty)$.
Work Step by Step
Step 1. For $2x^2+7x-4\ge0 \Longrightarrow (2x-1)(x+4)\ge0$, identify boundary points as $x=-4,\frac{1}{2}$.
Step 2. Form intervals $(-\infty,-4],[-4,\frac{1}{2}],[\frac{1}{2},\infty)$.
Step 3. Choose test values for each interval $x=-5,0,1$.
Step 4. Test the inequality to get results: $True,\ False,\ True$
Step 5. We have the solution $(-\infty,-4]\cup[\frac{1}{2},\infty)$.
