Answer
$(-\infty,\frac{1}{2})\cup[\frac{7}{5},\infty)$
Work Step by Step
Step 1. Rewrite the inequality as
$\frac{x+4}{2x-1}-3\leq0$
which gives
$\frac{x+4-6x+3}{2x-1}\leq0$, $\frac{-5x+7}{2x-1}\leq0$
and
$\frac{5x-7}{2x-1}\geq0$
Thus the boundary points are $x=1/2,7/5$
Step 2. Using the test points to examine signs across the boundary points, we have
$...(+)...(1/2)...(-)...(7/5)...(+)...$
Thus the solutions are
$x\lt\frac{1}{2}$ plus $x\geq\frac{7}{5}$
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 $(-\infty,\frac{1}{2})\cup[\frac{7}{5},\infty)$
