To solve the equation \(-9x + 1 = -71\), follow these steps:
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Subtract 1 from both sides of the equation:
\[ -9x + 1 - 1 = -71 - 1 \]
This simplifies to:
\[ -9x = -72 \]
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Next, divide both sides by -9:
\[ x = \frac{-72}{-9} \]
This simplifies to:
\[ x = 8 \]
So the solution to the equation \(-9x + 1 = -71\) is
\[ \boxed{8} \]