To solve the equation \( \frac{3}{2} - \frac{7}{4}v = -\frac{9}{8} \), follow these steps:

### Step 1: Isolate the term with \( v \)

First, subtract \( \frac{3}{2} \) from both sides of the equation:

\[
\frac{3}{2} - \frac{7}{4}v - \frac{3}{2} = -\frac{9}{8} - \frac{3}{2}
\]

\[
-\frac{7}{4}v = -\frac{9}{8} - \frac{3}{2}
\]

### Step 2: Simplify the right side

To combine the fractions on the right side, first express \( \frac{3}{2} \) with a common denominator of 8:

\[
\frac{3}{2} = \frac{12}{8}
\]

So the equation becomes:

\[
-\frac{7}{4}v = -\frac{9}{8} - \frac{12}{8}
\]

\[
-\frac{7}{4}v = -\frac{21}{8}
\]

### Step 3: Solve for \( v \)

To isolate \( v \), multiply both sides by the reciprocal of \( -\frac{7}{4} \), which is \( -\frac{4}{7} \):

\[
v = -\frac{4}{7} \times -\frac{21}{8}
\]

### Step 4: Simplify the multiplication

\[
v = \frac{4 \times 21}{7 \times 8}
\]

\[
v = \frac{84}{56}
\]

Simplify the fraction:

\[
v = \frac{3}{2}
\]

So, the solution is \( v = \frac{3}{2} \).

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions you might find interesting:
1. How would the solution change if the right side were positive, \( \frac{9}{8} \) instead of \( -\frac{9}{8} \)?
2. What if the equation were \( \frac{3}{2} + \frac{7}{4}v = -\frac{9}{8} \)?
3. How would you solve \( \frac{7}{4}v + \frac{3}{2} = 0 \)?
4. How does multiplying both sides by the reciprocal of a fraction affect the solution?
5. Can you express \( v \) as a decimal rather than a fraction?

**Tip:** Always convert fractions to have a common denominator when adding or subtracting them.

Learn how to solve the equation 3/2 - 7/4v = -9/8 step-by-step with a detailed solution. This problem involves equations with fractions and multiplication of fractions. Suitable for students in Grades 7-9.

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