  4𝑥 − 2( 𝑥 + 1 ) = 2𝑦 − 4𝑥 

Let's solve the equation step by step:

### Given equation:
\[
4x - 2(x + 1) = 2y - 4x
\]

1. **Distribute the \(-2\) on the left-hand side**:
   \[
   4x - 2x - 2 = 2y - 4x
   \]

2. **Simplify the left-hand side**:
   \[
   (4x - 2x) - 2 = 2y - 4x
   \]
   \[
   2x - 2 = 2y - 4x
   \]

3. **Add \(4x\) to both sides to move all \(x\) terms to the left-hand side**:
   \[
   2x + 4x - 2 = 2y
   \]
   \[
   6x - 2 = 2y
   \]

4. **Add 2 to both sides** to isolate the \(6x\) term:
   \[
   6x = 2y + 2
   \]

5. **Solve for \(y\)** by dividing both sides by 2:
   \[
   y = 3x - 1
   \]

### Final solution:
\[
y = 3x - 1
\]

Would you like more details or have any questions?

Here are 5 related questions to further explore:
1. How would the solution change if the constant term was different?
2. Can you rewrite the equation in terms of \(x\)?
3. What is the graphical representation of \(y = 3x - 1\)?
4. How do you solve if there were fractions in the equation?
5. How does distributing negative values affect solving equations?

**Tip:** When simplifying, always perform distribution before combining like terms to avoid errors!

4𝑥 − 2( 𝑥 + 1 ) = 2𝑦 − 4𝑥

Learn how to solve the linear equation 4x - 2(x + 1) = 2y - 4x with a detailed, step-by-step solution. This problem covers important algebraic concepts like distributing terms, combining like terms, and solving for y. Suitable for students in Grades 8-10.

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