1. **State the problem:** Solve the equation $$\frac{7}{5} - \frac{1}{3} v = -\frac{3}{4}$$ for $v$. 2. **Isolate the term with $v$:** Move $\frac{7}{5}$ to the right side by subtracting it from both sides: $$-\frac{1}{3} v = -\frac{3}{4} - \frac{7}{5}$$ 3. **Find a common denominator to combine the right side:** The denominators are 4 and 5, so the common denominator is 20. $$-\frac{3}{4} = -\frac{15}{20}, \quad \frac{7}{5} = \frac{28}{20}$$ 4. **Combine the fractions:** $$-\frac{15}{20} - \frac{28}{20} = -\frac{43}{20}$$ So, $$-\frac{1}{3} v = -\frac{43}{20}$$ 5. **Solve for $v$ by dividing both sides by $-\frac{1}{3}$:** Dividing by a fraction is the same as multiplying by its reciprocal: $$v = \frac{-\frac{43}{20}}{-\frac{1}{3}} = -\frac{43}{20} \times -3 = \frac{43}{20} \times 3$$ 6. **Multiply the fractions:** $$v = \frac{43 \times 3}{20} = \frac{129}{20}$$ 7. **Simplify if possible:** $129$ and $20$ have no common factors other than 1, so the fraction is in simplest form. **Final answer:** $$v = \frac{129}{20}$$