To find out which equation has a solution of \( x = -12 \), we can substitute \( -12 \) into each equation and see if the equation holds true.
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Equation: \( x - 1 = -12 \) \[ -12 - 1 = -13 \quad \text{(not true)} \]
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Equation: \( x - 1 = -\frac{1}{2} \) \[ -12 - 1 = -13 \quad \text{(not true)} \]
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Equation: \( x + 12 = -1 \) \[ -12 + 12 = 0 \quad \text{(not true)} \]
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Equation: \( x + \frac{1}{2} = -1 \) \[ -12 + \frac{1}{2} = -\frac{24}{2} + \frac{1}{2} = -\frac{23}{2} \quad \text{(not true)} \]
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Equation: \( x - 12 = 1 \) \[ -12 - 12 = -24 \quad \text{(not true)} \]
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Equation: \( x + 1 = 12 \) \[ -12 + 1 = -11 \quad \text{(not true)} \]
None of the equations you provided correctly solve to give a solution of \( x = -12 \).
It seems there has been a misunderstanding because none of the equations lead to the solution \( x = -12 \). Please provide correct options if needed.