Answer
$$-1\lt x \leq\frac{1}{3}$$
Work Step by Step
We have $$-\frac{1}{3}\lt\frac{3x+1}{6}\leq\frac{1}{3}$$
Solving $$-\frac{1}{3}*6\lt3x+1\leq\frac{1}{3}*6$$ $$-2-1\lt3x\leq2-1$$ $$-\frac{3}{3}\lt x \leq\frac{1}{3}$$ $$-1\lt x \leq\frac{1}{3}$$