Answer
$-3\lt x\lt \frac{1}{2}$
Work Step by Step
Step 1. Factoring the inequality as $(2x-1)(x+3)\lt0$, we can identify the boundary points as $x=-3,\frac{1}{2}$
Step 2. Use test points to examine the signs of the left side across the boundary points; we have $...(+)...(-3)...(-)...(\frac{1}{2})...(+)...$; thus the solutions are $-3\lt x\lt \frac{1}{2}$
Step 3. We can graph the solution on a real number line as shown in the figure.
