https://file.aiquickdraw.com/mathbot/file/172675194566768tt94ok.jpg

Let's solve the equation provided in the image:

\[
6n - 6 = 3n + 6
\]

### Step-by-Step Solution:
1. Subtract \(3n\) from both sides to collect like terms:
\[
6n - 3n - 6 = 6
\]
This simplifies to:
\[
3n - 6 = 6
\]

2. Add 6 to both sides to isolate the \(3n\) term:
\[
3n - 6 + 6 = 6 + 6
\]
Simplifying further:
\[
3n = 12
\]

3. Divide both sides by 3 to solve for \(n\):
\[
n = \frac{12}{3} = 4
\]

### Final Answer:
\[
n = 4
\]

Would you like further clarification or additional details?

Here are five related questions you can explore:
1. What happens if you have variables on both sides with coefficients other than 1?
2. How do you check if your solution for \(n\) is correct?
3. Can you solve similar equations with fractions or decimals?
4. What if the equation had no solutions? How would that be identified?
5. How would you solve equations with higher powers of \(n\), such as \(n^2\)?

**Tip:** Always simplify equations step by step and keep the variable terms on one side and constants on the other.

Learn how to solve the linear equation 6n - 6 = 3n + 6 with a detailed step-by-step solution. This problem demonstrates key algebraic concepts, including combining like terms and isolating variables. Ideal for students in Grades 7-8.

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