Solve For V A71608

1. **State the problem:** Solve the equation $$\frac{v}{3} = \frac{v}{4} - 3$$ for $v$. 2. **Identify the formula and rules:** This is a linear equation with fractions. To solve, we first eliminate the fractions by finding a common denominator and then isolate $v$. 3. **Eliminate fractions:** The denominators are 3 and 4. The least common denominator (LCD) is 12. Multiply both sides of the equation by 12: $$12 \times \frac{v}{3} = 12 \times \left(\frac{v}{4} - 3\right)$$ 4. **Simplify each term:** $$12 \times \frac{v}{3} = 4v$$ $$12 \times \frac{v}{4} = 3v$$ $$12 \times (-3) = -36$$ So the equation becomes: $$4v = 3v - 36$$ 5. **Isolate $v$:** Subtract $3v$ from both sides: $$4v - 3v = 3v - 3v - 36$$ $$\cancel{4v} - \cancel{3v} = -36$$ $$v = -36$$ 6. **Final answer:** $$v = -36$$