Let's solve the equation step by step:

\[
-\frac{3}{4}v - \frac{7}{4} = 4v - \frac{2}{3}
\]

### Step 1: Eliminate fractions
To eliminate the fractions, find the least common denominator (LCD) of 4 and 3. The LCD of 4 and 3 is 12. Multiply the entire equation by 12 to get rid of the denominators:

\[
12 \times \left(-\frac{3}{4}v\right) - 12 \times \left(\frac{7}{4}\right) = 12 \times 4v - 12 \times \left(\frac{2}{3}\right)
\]

Simplify each term:
\[
12 \times \left(-\frac{3}{4}v\right) = -9v, \quad 12 \times \left(\frac{7}{4}\right) = 21, \quad 12 \times 4v = 48v, \quad 12 \times \left(\frac{2}{3}\right) = 8
\]

So the equation becomes:
\[
-9v - 21 = 48v - 8
\]

### Step 2: Move variable terms to one side
Add \(9v\) to both sides to collect the variable terms on one side:
\[
-21 = 57v - 8
\]

### Step 3: Move constant terms to the other side
Add \(8\) to both sides:
\[
-21 + 8 = 57v
\]
\[
-13 = 57v
\]

### Step 4: Solve for \(v\)
Divide both sides by 57:
\[
v = \frac{-13}{57}
\]

This fraction can be simplified:
\[
v = \frac{-13}{57} = \frac{-13}{57} \div 13 = \frac{-1}{3}
\]

So, the solution is:
\[
v = -\frac{1}{3}
\]

Would you like a detailed explanation of any step?

### Related Questions:
1. How can you solve an equation with multiple fractions more easily?
2. What are the steps to simplify a fraction like \(-\frac{13}{57}\)?
3. How do you determine the least common denominator between two numbers?
4. What are common mistakes to avoid when solving equations with fractions?
5. How can you verify if a solution to an equation is correct?

### Tip:
When dealing with fractions in an equation, clearing the denominators by multiplying through by the least common denominator is a powerful technique to simplify the process.

Explore how to solve the algebraic equation -3/4v - 7/4 = 4v - 2/3 with fractions step by step. This guide covers the Least Common Denominator (LCD) method for eliminating fractions and provides a simplified solution for v = -1/3. Ideal for students in Grades 8-10.

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