To solve the equation:

\[
-2x + 1 = -x + 7
\]

Let's follow these steps:

### Step 1: Move all terms involving \(x\) to one side and constants to the other side.
We can do this by adding \(2x\) to both sides:

\[
1 = -x + 7 + 2x
\]

Simplify:

\[
1 = x + 7
\]

### Step 2: Subtract 7 from both sides to isolate \(x\):

\[
1 - 7 = x
\]

Simplify:

\[
-6 = x
\]

### Final Answer:
\[
x = -6
\]

Would you like a detailed explanation of any step?

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Here are 5 related questions to expand on this:

1. How would the solution change if the equation was \(-2x + 1 = -x + 10\)?
2. Can you solve \(3x - 5 = -x + 8\)?
3. What happens if you add a constant to both sides of an equation?
4. How do you check if your solution to an equation is correct?
5. How do you solve equations with fractions?

**Tip:** Always double-check your solution by substituting the value of \(x\) back into the original equation.

Learn how to solve the linear equation -2x + 1 = -x + 7 with a step-by-step explanation. This solution covers key algebraic concepts, including moving terms to isolate variables and simplifying expressions. Suitable for students in Grades 6-8.

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