To find which equation has a solution of \(-12\), we can substitute \(-12\) into each equation and see if the left-hand side equals the right-hand side.
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Equation: \(x - 12 = 1\) \[ -12 - 12 = -24 \quad (\text{not equal to } 1) \]
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Equation: \(x - \frac{1}{2} = 1\) \[ -12 - \frac{1}{2} = -12.5 \quad (\text{not equal to } 1) \]
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Equation: \(x + 12 = -1\) \[ -12 + 12 = 0 \quad (\text{not equal to } -1) \]
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Equation: \(x + \frac{1}{2} = -1\) \[ -12 + \frac{1}{2} = -11.5 \quad (\text{not equal to } -1) \]
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Equation: \(x - 1 = -12\) \[ -12 - 1 = -13 \quad (\text{not equal to } -12) \]
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Equation: \(x + 1 = 12\) \[ -12 + 1 = -11 \quad (\text{not equal to } 12) \]
None of the equations yield a valid solution for \(x = -12\).
Let’s correct the calculations and look for the equation that resolves to \(-12\):
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For \(x - 12 = 1\) \[ x = 1 + 12 = 13 \]
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For \(x - \frac{1}{2} = 1\) \[ x = 1 + \frac{1}{2} = 1.5 \]
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For \(x + 12 = -1\) \[ x = -1 - 12 = -13 , \text{(does not match)} \]
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For \(x + \frac{1}{2} = -1\) \[ x = -1 - \frac{1}{2} = -1.5 , \text{(does not match)} \]
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For \(x - 1 = -12\) \[ x = -12 + 1 = -11 , \text{(does not match)} \]
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For \(x + 1 = 12\) \[ x = 12 - 1 = 11 , \text{(does not match)} \]
There seems to be mixed results. It appears the intended choice is x-1=-12 which gives:
Correct Option: x - 1 = -12 gives the result -12. Therefore the equations with \( -12 \) would possibly be incorrect in structure. Errors may be present in framing the equation options. I apologize for the confusion. The actual computations indicate that a reevaluation is required due to wrong coefficient placements or option types. Based on existing solutions, none correctly yield x=-12 correctly, please share options if discrepancies persist.