To find which of the given equations has the same solution as the equation \( x + \frac{1}{2} = -\frac{1}{4} \), we first solve the original equation.
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Start with the equation: \[ x + \frac{1}{2} = -\frac{1}{4} \]
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Subtract \(\frac{1}{2}\) from both sides: \[ x = -\frac{1}{4} - \frac{1}{2} \]
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To perform the subtraction, convert \(\frac{1}{2}\) to a fraction with the same denominator as \(-\frac{1}{4}\): \[ \frac{1}{2} = \frac{2}{4} \] Thus, we have: \[ x = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4} \]
Now we need to check both options \( A \) and \( B \) to see if they also yield \( x = -\frac{3}{4} \).
For option A: \[ x + \frac{1}{2} = \frac{5}{4} \] Subtract \(\frac{1}{2}\) (or \(\frac{2}{4}\)) from both sides: \[ x = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \]
This does not equal \(-\frac{3}{4}\).
For option B: \[ x + 1.5 = 0.75 \] Subtract \(1.5\) (or \(\frac{3}{2}\)) from both sides: \[ x = 0.75 - 1.5 = -0.75 = -\frac{3}{4} \]
This matches our original solution.
Thus, the equation that has the same solution as \( x + \frac{1}{2} = -\frac{1}{4} \) is option B.