To solve the equation \(-3x - 6 = -7x + 34\), follow these steps:
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Add \(7x\) to both sides to get all terms involving \(x\) on one side:
\[ -3x + 7x - 6 = 34 \]
This simplifies to:
\[ 4x - 6 = 34 \]
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Add \(6\) to both sides to isolate the term with \(x\):
\[ 4x - 6 + 6 = 34 + 6 \]
This simplifies to:
\[ 4x = 40 \]
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Divide by \(4\) to solve for \(x\):
\[ x = \frac{40}{4} \]
So,
\[ x = 10 \]
The solution to the equation \(-3x - 6 = -7x + 34\) is \(x = 10\).