To determine which equation has a solution of \(-\frac{11}{4}\), we can substitute \(-\frac{11}{4}\) into each equation and check if it holds true.
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Equation: \(-\frac{1}{2}x = \frac{11}{2}\) \[ -\frac{1}{2}\left(-\frac{11}{4}\right) = \frac{11}{2} \] \[ \frac{11}{8} \neq \frac{11}{2} \quad \text{(False)} \]
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Equation: \(-2x = \frac{11}{2}\) \[ -2\left(-\frac{11}{4}\right) = \frac{11}{2} \] \[ \frac{22}{4} = \frac{11}{2} \quad \text{(True)} \]
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Equation: \(\frac{1}{2}x = -11\) \[ \frac{1}{2}\left(-\frac{11}{4}\right) = -11 \] \[ -\frac{11}{8} \neq -11 \quad \text{(False)} \]
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Equation: \(-2x = \frac{2}{11}\) \[ -2\left(-\frac{11}{4}\right) = \frac{2}{11} \] \[ \frac{22}{4} = \frac{11}{2} \neq \frac{2}{11} \quad \text{(False)} \]
From the evaluations, the second equation \(-2x = \frac{11}{2}\) is the only one that gives \(-\frac{11}{4}\) as a solution.
Thus, the correct response is: \(-2x = \frac{11}{2}\)