To solve the equation \(-x - 10 = 3x + 20\), follow these steps:
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Add \(x\) to both sides to eliminate the \(-x\) on the left side: \[ -x + x - 10 = 3x + x + 20 \] This simplifies to: \[ -10 = 4x + 20 \]
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Subtract 20 from both sides to isolate terms containing \(x\): \[ -10 - 20 = 4x + 20 - 20 \] This simplifies to: \[ -30 = 4x \]
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Divide both sides by 4 to solve for \(x\): \[ x = \frac{-30}{4} \] Simplifying gives: \[ x = -\frac{15}{2} \quad \text{or} \quad x = -7.5 \]
Thus, the solution is: \[ x = -\frac{15}{2} \quad \text{or} \quad x = -7.5 \]