To solve the equation \(-x + 8 = x - 2\), follow these steps:

### Step 1: Move all terms involving \(x\) to one side of the equation.
Add \(x\) to both sides to get rid of the \(-x\) on the left:
\[
-x + 8 + x = x - 2 + x
\]
This simplifies to:
\[
8 = 2x - 2
\]

### Step 2: Move constant terms to the other side.
Add 2 to both sides to eliminate the \(-2\) on the right:
\[
8 + 2 = 2x - 2 + 2
\]
This simplifies to:
\[
10 = 2x
\]

### Step 3: Solve for \(x\).
Divide both sides by 2:
\[
\frac{10}{2} = \frac{2x}{2}
\]
This gives:
\[
x = 5
\]

### Final Answer:
\[
x = 5
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. What happens if we substitute \(x = 5\) back into the original equation?
2. How would the solution change if the equation were \( -2x + 8 = x - 2 \)?
3. Can you solve the equation \(3x + 7 = 2x - 5\)?
4. How do you solve the equation \(4x - 10 = 2x + 6\)?
5. What is the general method for solving linear equations with variables on both sides?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure both sides are equal.

Learn how to solve the equation -x + 8 = x - 2 step-by-step with detailed explanations and solutions. This problem covers linear equations with variables on both sides. Suitable for Grades 7-9 students and anyone interested in solving linear equations.

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