## Precalculus (6th Edition) Blitzer

$(-4,\frac{3}{2})$
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.