To solve the equation \( 6(-3 - x) - 2x = 14 \), follow these steps:
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Distribute the 6: \[ 6 \cdot -3 + 6 \cdot -x - 2x = 14 \] This simplifies to: \[ -18 - 6x - 2x = 14 \]
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Combine like terms: \[ -18 - 8x = 14 \]
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Add 18 to both sides: \[ -8x = 14 + 18 \] This simplifies to: \[ -8x = 32 \]
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Divide both sides by -8: \[ x = \frac{32}{-8} = -4 \]
Thus, the value of \( x \) is \(\boxed{-4}\).