https://file.aiquickdraw.com/mathbot/file/1728046617959hu7aj1zq.jpg

The equation from the image is:

\[
5(1 + 2y) = \frac{1}{2}(7 + 40y)
\]

### Steps to solve for \( y \):

1. **Distribute on both sides**:
   - Left side: \( 5(1 + 2y) = 5 + 10y \)
   - Right side: \( \frac{1}{2}(7 + 40y) = \frac{7}{2} + 20y \)

   The equation becomes:
   \[
   5 + 10y = \frac{7}{2} + 20y
   \]

2. **Eliminate the fraction** by multiplying through by 2 to clear the denominator:
   \[
   2(5 + 10y) = 2\left(\frac{7}{2} + 20y\right)
   \]
   Simplifies to:
   \[
   10 + 20y = 7 + 40y
   \]

3. **Isolate terms involving \( y \)**:
   - Subtract \( 20y \) from both sides:
     \[
     10 = 7 + 20y
     \]
   - Subtract 7 from both sides:
     \[
     3 = 20y
     \]

4. **Solve for \( y \)** by dividing both sides by 20:
   \[
   y = \frac{3}{20}
   \]

So, the solution is \( y = \frac{3}{20} \).

Would you like more details on any step or have any further questions?

### Related Questions:
1. How do you solve linear equations with fractions?
2. What are the properties of equality used in this solution?
3. How can you check your solution in an equation?
4. What is the importance of distributing terms correctly in algebra?
5. How do you solve equations with variables on both sides?

### Tip:
When solving equations with fractions, it's often helpful to eliminate the fraction early by multiplying both sides by the denominator.

Learn how to solve a linear equation with fractions: 5(1 + 2y) = 1/2(7 + 40y). This problem uses the distributive property and fraction elimination techniques to find the value of y. Suitable for students in Grades 8-10.

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