To solve the equation \(-4(3x + 10) - 2 = 54\), follow these steps:
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Distribute \(-4\) to the terms inside the parentheses: \[ -4 \cdot 3x - 4 \cdot 10 - 2 = 54 \] This simplifies to: \[ -12x - 40 - 2 = 54 \]
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Combine the constants on the left side: \[ -12x - 42 = 54 \]
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Next, add \(42\) to both sides of the equation to isolate the term with \(x\): \[ -12x - 42 + 42 = 54 + 42 \] This simplifies to: \[ -12x = 96 \]
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Finally, divide both sides by \(-12\) to solve for \(x\): \[ x = \frac{96}{-12} \] This simplifies to: \[ x = -8 \]
Thus, the solution to the equation is: \[ \boxed{-8} \]