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.