To determine which equation has a solution of \(-\frac{1}{2}\), we can substitute \(-\frac{1}{2}\) into each equation and check if it satisfies the equation.
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First equation: \[ x - 1 = -\frac{1}{2} \] Substitute \(x = -\frac{1}{2}\): \[ -\frac{1}{2} - 1 = -\frac{1}{2} \implies -\frac{1}{2} - \frac{2}{2} = -\frac{3}{2} \quad (\text{not correct}) \]
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Second equation: \[ x - \frac{1}{2} = 1 \] Substitute \(x = -\frac{1}{2}\): \[ -\frac{1}{2} - \frac{1}{2} = 1 \implies -1 = 1 \quad (\text{not correct}) \]
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Third equation: \[ x + 1 = \frac{1}{2} \] Substitute \(x = -\frac{1}{2}\): \[ -\frac{1}{2} + 1 = \frac{1}{2} \implies \frac{1}{2} = \frac{1}{2} \quad (\text{correct}) \]
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Fourth equation: \[ x + \frac{1}{2} = -1 \] Substitute \(x = -\frac{1}{2}\): \[ -\frac{1}{2} + \frac{1}{2} = -1 \implies 0 = -1 \quad (\text{not correct}) \]
The third equation \(x + 1 = \frac{1}{2}\) has a solution of \(-\frac{1}{2}\).
1 answer