To solve the equation \(-2x + 8 = -x + 7\), we can follow these steps:
- Add \(x\) to both sides to eliminate \(-x\) from the right side:
\[ -2x + 8 + x = -x + 7 + x \]
This simplifies to:
\[ -2x + x + 8 = 7 \]
So we have:
\[ -x + 8 = 7 \]
- Subtract 8 from both sides to isolate the term with \(x\):
\[ -x + 8 - 8 = 7 - 8 \]
This simplifies to:
\[ -x = -1 \]
- Multiply both sides by -1 to solve for \(x\):
\[ x = 1 \]
Thus, the solution to the equation is \(\boxed{1}\).
To verify, we can substitute \(x = 1\) into the original equation:
Left side: \[ -2(1) + 8 = -2 + 8 = 6 \]
Right side: \[ -(1) + 7 = -1 + 7 = 6 \]
Both sides are equal, confirming that \(x = 1\) is correct.