To solve the equation \(-5x + 6 = -7x - 2\), follow these steps:
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Add \(7x\) to both sides:
\[ -5x + 7x + 6 = -2 \]
This simplifies to:
\[ 2x + 6 = -2 \]
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Subtract 6 from both sides:
\[ 2x + 6 - 6 = -2 - 6 \]
This simplifies to:
\[ 2x = -8 \]
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Divide both sides by 2:
\[ x = \frac{-8}{2} \]
Which simplifies to:
\[ x = -4 \]
So, the solution to the equation \(-5x + 6 = -7x - 2\) is
\[ \boxed{-4}. \]