Answer
$(-4,\frac{3}{2})$
Work Step by Step
Step 1. Rewrite the inequality as
$2x^2+5x-12\lt0$ or $(2x-3)(x+4)\lt0$
We can identify the boundary points as: $x=-4, \frac{3}{2}$
Step 2. Using test points to examine the signs of the left side across the boundary points, we have
$...(+)...(-4)...(-)...(\frac{3}{2})...(+)...$
and the solutions are $(-4,\frac{3}{2})$
Step 3. We can graph the solutions on a real number line as shown in the figure.
