We are given the equation:

\[
\frac{3}{4} = \frac{4y - 2}{5}
\]

We need to solve for \( y \).

### Step-by-step solution:

1. Cross-multiply to eliminate the fractions:
   \[
   3 \times 5 = 4 \times (4y - 2)
   \]
   This simplifies to:
   \[
   15 = 16y - 8
   \]

2. Add 8 to both sides to isolate the term with \( y \):
   \[
   15 + 8 = 16y
   \]
   \[
   23 = 16y
   \]

3. Divide both sides by 16 to solve for \( y \):
   \[
   y = \frac{23}{16}
   \]

Thus, the solution is:
\[
y = \frac{23}{16}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve proportions with variables on both sides?
2. What is cross-multiplication, and why does it work?
3. How do you handle equations with fractions?
4. How do you simplify complex fractions before solving equations?
5. What are common errors to avoid when solving for variables in proportions?

**Tip:** Always double-check your solution by substituting it back into the original equation to verify its correctness.

Learn how to solve the proportion 3/4 = (4y - 2)/5 using cross-multiplication and linear equation solving. This step-by-step solution explains the process, including handling fractions and isolating variables. Ideal for students in Grades 6-8.

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