Let's solve the equation \( 12 - 8n = 8 - 10n \).

### Step 1: Simplify both sides
First, let's get all the terms involving \( n \) on one side of the equation and the constant terms on the other side.

\[
12 - 8n = 8 - 10n
\]

Add \( 10n \) to both sides to move the \( n \)-terms to one side:

\[
12 - 8n + 10n = 8
\]

This simplifies to:

\[
12 + 2n = 8
\]

### Step 2: Isolate the variable
Next, subtract 12 from both sides to move the constant term to the right:

\[
2n = 8 - 12
\]

Simplify the right side:

\[
2n = -4
\]

Finally, divide both sides by 2 to solve for \( n \):

\[
n = \frac{-4}{2} = -2
\]

### Solution:
The solution to the equation is \( n = -2 \).

Would you like more details, or do you have any questions?

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Here are 5 related questions:
1. What happens if you add 8n to both sides instead of 10n?
2. How would you solve the equation if it was \( 12 - 8n = 10n - 8 \)?
3. What does it mean when the solution to an equation is a negative number?
4. Can this equation have more than one solution? Why or why not?
5. How can you check if your solution to the equation is correct?

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

Learn how to solve the linear equation 12 - 8n = 8 - 10n step-by-step with detailed explanations. This problem involves basic algebra concepts, focusing on solving linear equations. Suitable for students in Grades 6-8.

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