## Precalculus (6th Edition) Blitzer

$(-\infty,5)\cup(5,\frac{13}{2})$
Step 1. Rewrite the inequality as $(x-5)^2(x-\frac{13}{2})\lt0$ The boundary points are $x=5,\frac{13}{2}$ Step 2. Using the test points to examine signs across the boundary points, we have $...(-)...(5)...(-)...(\frac{13}{2})...(+)...$ Thus, the solutions are $x\lt\frac{13}{2}$ plus $x\ne5$ Step 3. We can express the solutions on a real number line as shown in the figure. Step 4. We can express the solutions in interval notation as $(-\infty,5)\cup(5,\frac{13}{2})$