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The image provided shows a math problem, specifically the equation \( y = \frac{2x}{2x+1} \) on the left side. Below the equation, there is another equation written as \( 2y = \frac{x+7}{2x+1} \).

### Problem Explanation and Solution:
1. **Given:** \( y = \frac{2x}{2x+1} \)
2. **To Solve:** \( 2y = \frac{x+7}{2x+1} \)

**Step 1:** First, we know that \( y = \frac{2x}{2x+1} \). 
   
**Step 2:** Multiply both sides of the equation \( y = \frac{2x}{2x+1} \) by 2 to find \( 2y \):

\[
2y = 2 \times \frac{2x}{2x+1} = \frac{4x}{2x+1}
\]

**Step 3:** Now, compare \( 2y = \frac{4x}{2x+1} \) with the given \( 2y = \frac{x+7}{2x+1} \).

Since the right sides of the equations must be equal, we can equate:

\[
\frac{4x}{2x+1} = \frac{x+7}{2x+1}
\]

**Step 4:** Since the denominators are the

Explore a step-by-step solution to solving the equations y = (2x) / (2x + 1) and 2y = (x + 7) / (2x + 1). This problem involves key algebraic concepts suitable for Grades 9-10.

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