Answer
$-\frac{9}{2}\lt x\lt\frac{15}{2}$
See graph
Work Step by Step
For
$$-4\lt\frac{2x-3}{3}$$
$$-12\lt2x-3$$
$$-12+3\lt2x-3+3$$
$$-9\lt 2x$$
$$\frac{-9}{2}\lt\frac{2x}{2}$$
$$-\frac{9}{2}\lt x$$
$$x\gt-\frac{9}{2}$$
For
$$\frac{2x-3}{3}\lt4$$
$$2x-3\lt12$$
$$2x-3+3\lt12+3$$
$$2x\lt15$$
$$\frac{2x}{2}\lt\frac{15}{2}$$
$$x\lt\frac{15}{2}$$
Then, combining:
$$x\gt-\frac{9}{2}\text{ and }x\lt\frac{15}{2}$$
$$-\frac{9}{2}\lt x\lt\frac{15}{2}$$
The graph is as shown.
