Let's solve the equation step by step:

### Given equation:
\[
3y - y + 2y - 5 = 7 - 2y + 5
\]

1. **Simplify both sides:**

- On the left-hand side: 
  \[
  3y - y + 2y - 5 = (3y - y + 2y) - 5 = 4y - 5
  \]
  
- On the right-hand side: 
  \[
  7 - 2y + 5 = (7 + 5) - 2y = 12 - 2y
  \]

So, the equation becomes:
\[
4y - 5 = 12 - 2y
\]

2. **Move all terms involving \(y\) to one side:**
   Add \(2y\) to both sides:
   \[
   4y + 2y - 5 = 12
   \]
   \[
   6y - 5 = 12
   \]

3. **Move constant terms to the other side:**
   Add 5 to both sides:
   \[
   6y = 12 + 5
   \]
   \[
   6y = 17
   \]

4. **Solve for \(y\):**
   Divide both sides by 6:
   \[
   y = \frac{17}{6}
   \]

### Final solution:
\[
y = \frac{17}{6}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand this topic:
1. How do you solve equations with variables on both sides?
2. How can you verify the solution to an equation?
3. How do you solve equations involving fractions?
4. What are some techniques for solving linear equations efficiently?
5. What happens when an equation has no solution or infinite solutions?

**Tip:** Always simplify both sides of an equation before moving terms to isolate the variable. This helps to avoid mistakes and makes solving easier.

Learn how to solve the linear equation 3y - y + 2y - 5 = 7 - 2y + 5 step by step. This guide covers core algebraic concepts such as combining like terms, moving variables, and solving for y. Suitable for middle school students in Grades 6-8.

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