To solve the equation \( n = 2k - 2n \) for \( n \), let's proceed step-by-step:

### Step 1: Combine Like Terms
Start by adding \( 2n \) to both sides of the equation to move all \( n \) terms to one side:

\[
n + 2n = 2k
\]

\[
3n = 2k
\]

### Step 2: Solve for \( n \)
Now, divide both sides by 3 to isolate \( n \):

\[
n = \frac{2k}{3}
\]

### Final Answer
\[
n = \frac{2k}{3}
\]

This is the solution for \( n \) in terms of \( k \).

Would you like more details or have any questions about this solution?

Here are some related questions you might find interesting:

1. What is the value of \( n \) when \( k = 9 \)?
2. How would you solve for \( k \) in terms of \( n \)?
3. Can this formula be applied if \( k \) is a negative number?
4. How does the equation change if an additional constant term is added to the right side?
5. What are some practical applications where such linear equations are useful?

**Tip:** Always check the validity of your solution by substituting it back into the original equation.

Learn how to solve the linear equation n = 2k - 2n with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and algebraic manipulation. Suitable for students in Grades 9-12.

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