To solve the equation \( 2(x + 1) = 2 - y + 2x \), we will simplify and isolate the variable \(y\).

### Step 1: Expand both sides
First, expand the left-hand side:
\[
2(x + 1) = 2x + 2
\]
So the equation becomes:
\[
2x + 2 = 2 - y + 2x
\]

### Step 2: Simplify the equation
Now, subtract \( 2x \) from both sides to eliminate \( 2x \) from the equation:
\[
2 = 2 - y
\]

### Step 3: Isolate \(y\)
Subtract 2 from both sides:
\[
0 = -y
\]
Thus:
\[
y = 0
\]

### Final Solution:
The solution is \( y = 0 \).

Would you like a more detailed explanation or have any questions? 

Here are some related questions for further practice:
1. How would you solve an equation where both sides involve the same variable \( x \) (e.g., \( 3x + 5 = 7x - 1 \))?
2. What happens if we have a more complex equation like \( 3(x - 2) = 4 + 2x \)?
3. How can you check if your solution \( y = 0 \) is correct by substituting it back into the original equation?
4. What is the method for solving equations with multiple variables (e.g., \( 2x + 3y = 6 \))?
5. How do you approach solving inequalities involving variables?

**Tip:** Always simplify and combine like terms on both sides of an equation before attempting to isolate variables.

Explore how to solve the linear equation 2(x + 1) = 2 - y + 2x by expanding, simplifying, and isolating the variable y. This problem introduces concepts in algebra and variable isolation, suitable for students in Grades 7-9.

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