1. **State the problem:** Solve for $v$ in the equation $$\frac{5v}{7} = -25$$. 2. **Formula and rules:** To isolate $v$, multiply both sides of the equation by 7 to cancel the denominator. 3. **Multiply both sides by 7:** $$7 \times \frac{5v}{7} = 7 \times (-25)$$ This simplifies to: $$\cancel{7} \times \frac{5v}{\cancel{7}} = -175$$ 4. **Simplify the left side:** $$5v = -175$$ 5. **Divide both sides by 5 to solve for $v$:** $$v = \frac{-175}{5}$$ 6. **Simplify the fraction:** $$v = -35$$ **Final answer:** $$v = -35$$