1. **State the problem:** Solve the inequality $$-\frac{1}{3} + v \leq \frac{3}{5}$$ for the variable $v$. 2. **Recall the additive property of inequality:** You can add the same number to both sides of an inequality without changing the inequality's direction. 3. **Add $\frac{1}{3}$ to both sides to isolate $v$:** $$-\frac{1}{3} + v + \frac{1}{3} \leq \frac{3}{5} + \frac{1}{3}$$ 4. **Simplify the left side:** $$v \leq \frac{3}{5} + \frac{1}{3}$$ 5. **Find a common denominator to add the fractions on the right side:** The least common denominator of 5 and 3 is 15. $$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$$ $$\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$$ 6. **Add the fractions:** $$\frac{9}{15} + \frac{5}{15} = \frac{9 + 5}{15} = \frac{14}{15}$$ 7. **Final solution:** $$v \leq \frac{14}{15}$$ This means $v$ can be any number less than or equal to $\frac{14}{15}$.