Answer
$-3\leq x\leq4$
See graph
Work Step by Step
For
$$-1\leq\frac{-3x+5}{7}$$
$$-7\leq-3x+5$$
$$-7-5\leq-3x+5-5$$
$$-12\leq-3x$$
$$\frac{-12}{-3}\geq\frac{-3x}{-3}$$
$$4\geq x$$
$$x\leq 4$$
For
$$\frac{-3x+5}{7}\leq2$$
$$-3x+5\leq14$$
$$-3x+5-5\leq14-5$$
$$-3x\leq9$$
$$\frac{-3x}{-3}\geq\frac{9}{-3}$$
$$x\geq-3$$
Combining:
$$x\geq-3\text{ and }x\leq4$$
$$-3\leq x\leq4$$
The graph of the solution set is as shown.
