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