Answer
$-7\lt x\leq-\frac{1}{3}$
See graph
Work Step by Step
For
$$0\lt3(x+7)$$
$$0\lt 3x+21$$
$$0-21\lt3x+21-21$$
$$-21\lt3x$$
$$\frac{-21}{3}\lt\frac{3x}{3}$$
$$-7\lt x$$
$$x\gt-7$$
For
$$3(x+7)\leq20$$
$$3x+21\leq20$$
$$3x+21-21\leq20-21$$
$$3x\leq-1$$
$$\frac{3x}{3}\leq\frac{-1}{3}$$
$$x\leq-\frac{1}{3}$$
Then,
$$x\gt-7\text{ and }x\leq-\frac{1}{3}$$
$$-7\lt x\leq-\frac{1}{3}$$
The graph is as shown.
