To determine which equation has the solution of \( x = -\frac{11}{4} \), we can substitute \(-\frac{11}{4}\) into each equation and check if it satisfies the equation.
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For the equation \( -\frac{1}{2}x = \frac{11}{2} \): \[ -\frac{1}{2}\left(-\frac{11}{4}\right) = \frac{11}{2} \implies \frac{11}{8} \neq \frac{11}{2} \quad \text{(not a solution)} \]
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For the equation \( -2x = \frac{11}{2} \): \[ -2\left(-\frac{11}{4}\right) = \frac{11}{2} \implies \frac{22}{4} = \frac{11}{2} \quad \text{(this is a valid solution)} \]
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For the equation \( 12x = -11 \): \[ 12\left(-\frac{11}{4}\right) = -11 \implies -\frac{132}{4} = -11 \quad \text{(this is a valid solution)} \]
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For the equation \( -2x = \frac{2}{11} \): \[ -2\left(-\frac{11}{4}\right) = \frac{2}{11} \implies \frac{22}{4} = \frac{2}{11} \quad \text{(not a solution)} \]
Thus, the equations that have \( x = -\frac{11}{4} \) as a solution are:
- \( -2x = \frac{11}{2} \)
- \( 12x = -11 \)
If you can only select one, it seems more directly apparent that the second equation, \( -2x = \frac{11}{2} \), is the clearest match to the provided negative fraction solution.