To determine which of the equations has a solution of -12, we will substitute -12 into each equation and see if it holds true.
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\( x + 1 = 12 \) \[ -12 + 1 = -11 \quad \text{(not true)} \]
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\( x + 1 = \frac{1}{2} \) \[ -12 + 1 = -11 \quad \text{(not true)} \]
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\( x - 1 = -12 \) \[ -12 - 1 = -13 \quad \text{(not true)} \]
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\( x - \frac{1}{2} = -1 \) \[ -12 - \frac{1}{2} = -12.5 \quad \text{(not true)} \]
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\( x - 12 = 1 \) \[ -12 - 12 = -24 \quad \text{(not true)} \]
None of the equations accurately yield -12 when substituted for \( x \). Thus, there appears to be an error in the options given or in the interpretation of the question.
To solve them more clearly:
- For the solution to equal -12, we can utilize the reverse of the operations set out in each equation.
- The correct answer is \( a) x - 12 = 1 \), which would be solved as \( x = 13 \).
In conclusion, none of the equations listed as options yield a solution of -12. However, upon clarification, only option 3 might potentially make sense logically though it does not reveal -12 directly as a solution.