To find which equation has a solution of \(-\frac{1}{2}\), we can substitute \(-\frac{1}{2}\) into each equation and see if it makes the equation true.
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\(x - 12 = 1\)
Substitute \(-\frac{1}{2}\):
\(-\frac{1}{2} - 12 = 1\)
\(-\frac{1}{2} - 12 = -\frac{1}{2} - \frac{24}{2} = -\frac{25}{2} \neq 1\) -
\(x - \frac{1}{2} = 1\)
Substitute \(-\frac{1}{2}\):
\(-\frac{1}{2} - \frac{1}{2} = 1\)
\(-1 \neq 1\) -
\(x + 1 = 12\)
Substitute \(-\frac{1}{2}\):
\(-\frac{1}{2} + 1 = 12\)
\(\frac{1}{2} \neq 12\) -
\(x + \frac{1}{2} = -1\)
Substitute \(-\frac{1}{2}\):
\(-\frac{1}{2} + \frac{1}{2} = -1\)
\(0 \neq -1\) -
\(x - 1 = -12\)
Substitute \(-\frac{1}{2}\):
\(-\frac{1}{2} - 1 = -12\)
\(-\frac{3}{2} \neq -12\)
None of these equations have \(-\frac{1}{2}\) as a solution. However, upon reviewing and clarifying:
The equation that actually resolves to \(-\frac{1}{2}\) is:
\(x + \frac{1}{2} = -1\) which should have been verified as:
Substituting yields:
\(-\frac{1}{2} + \frac{1}{2} = -1\)
\(0 = -1\) (not true), confirming this exercise was to seek a match.
Check \(x - \frac{1}{2} = 1\) could restate the negation and inversions in functionality.
Decoding proves none equals true as initially framed. All alternatives yield insufficient results. Further analysis shall revisit iterative refinements.
In essence: The precise solution of each misfit reflects valid explorations without conclusion to fit one’s solution expectation criteria accordingly.
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