https://file.aiquickdraw.com/mathbot/file/1730362975572550mnymq.jpg

To solve the equation:

\[
\frac{3y}{2y - 1} = \frac{3}{4}
\]

we can follow these steps:

### Step 1: Cross-multiply
To eliminate the fractions, cross-multiply:

\[
3y \cdot 4 = 3 \cdot (2y - 1)
\]

### Step 2: Expand both sides
Multiply out each side:

\[
12y = 6y - 3
\]

### Step 3: Move terms involving \( y \) to one side
Subtract \( 6y \) from both sides:

\[
12y - 6y = -3
\]

\[
6y = -3
\]

### Step 4: Solve for \( y \)
Divide both sides by 6:

\[
y = -\frac{1}{2}
\]

### Final Answer
\[
y = -\frac{1}{2}
\]

Would you like further details or have any questions?

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Here are some related questions to explore:
1. How would you solve if the fractions had different constants?
2. What happens if both sides were complex fractions?
3. How would the solution change if the right side was zero?
4. What if \( y \) were in the denominator?
5. How would graphing this equation look?

**Tip:** Always check for potential restrictions in the denominator to avoid undefined values.

Solve \( \frac{3y}{2y - 1} = \frac{3}{4} \).

Learn how to solve the rational equation \( \frac{3y}{2y - 1} = \frac{3}{4} \) with a step-by-step solution using cross multiplication. This problem explores algebraic concepts suitable for Grades 8-10.

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