To find an expression equivalent to \(-\frac{5}{6}(x - \frac{1}{2}y + 12)\), we can distribute \(-\frac{5}{6}\) across each term inside the parentheses.
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Distributing to \(x\): \[ -\frac{5}{6} \cdot x = -\frac{5}{6}x \]
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Distributing to \(-\frac{1}{2}y\): \[ -\frac{5}{6} \cdot \left(-\frac{1}{2}y\right) = \frac{5}{12}y \]
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Distributing to \(12\): \[ -\frac{5}{6} \cdot 12 = -\frac{5 \cdot 12}{6} = -10 \]
Now, combine all the distributed terms: \[ -\frac{5}{6}x + \frac{5}{12}y - 10 \]
Thus, the expression equivalent to \(-\frac{5}{6}(x - \frac{1}{2}y + 12)\) is:
\[ -\frac{5}{6}x + \frac{5}{12}y - 10 \]
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