To expand \(-\frac{5}{6}(9b - 12)\), we will distribute \(-\frac{5}{6}\) to both terms inside the parentheses:
\[ -\frac{5}{6}(9b) - \frac{5}{6}(-12) \]
Calculating each term:
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For the first term: \[ -\frac{5}{6} \cdot 9b = -\frac{45b}{6} = -\frac{15b}{2} \quad \text{(simplifying)} \]
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For the second term: \[ -\frac{5}{6} \cdot (-12) = \frac{5 \cdot 12}{6} = \frac{60}{6} = 10 \]
Combining both results, we have:
\[ -\frac{15b}{2} + 10 \]
Thus, the expanded form is:
\[ -\frac{15b}{2} + 10 \]