Answer
$(-\infty,2)\cup(2,\frac{7}{2})$
Work Step by Step
Step 1. Rewrite the inequality as
$(x-2)^2(x-\frac{7}{2})\lt0$
The boundary points are:
$x=2,\frac{7}{2}$
Step 2. Using test points to examine signs across the boundary points, we have
$...(-)...(2)...(-)...(\frac{7}{2})...(+)...$
Thus the solutions are:
$x\lt\frac{7}{2}$ plus $x\ne2$
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 $(-\infty,2)\cup(2,\frac{7}{2})$
