Simplify the absolute value on the right side of the inequality.

$$-2 - \frac{3}{5}x \leq \left|\frac{1}{3}\right|$$ $$-2 - \frac{3}{5}x \leq \frac{1}{3}$$

$$- \frac{3}{5}x \leq \frac{1}{3} + 2$$

To add the numbers on the right side, find a common denominator.

$$- \frac{3}{5}x \leq \frac{1}{3} + \frac{6}{3}$$ $$- \frac{3}{5}x \leq \frac{7}{3}$$

Remember to reverse the inequality sign when multiplying or dividing by a negative number.

$$\left(-\frac{5}{3}\right) \left(-\frac{3}{5}x\right) \geq \left(\frac{7}{3}\right) \left(-\frac{5}{3}\right)$$ $$x \geq -\frac{35}{9}$$