To simplify the expression \( \frac{2}{5}(10x - 10y) - \frac{3}{4}(12x - 24y) \), follow these steps:
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Distribute the constants \( \frac{2}{5} \) and \( -\frac{3}{4} \) across the terms in the parentheses.
\[ \frac{2}{5}(10x - 10y) = \frac{2}{5} \cdot 10x - \frac{2}{5} \cdot 10y = \frac{20}{5}x - \frac{20}{5}y = 4x - 4y \]
\[ -\frac{3}{4}(12x - 24y) = -\frac{3}{4} \cdot 12x + \frac{3}{4} \cdot 24y = -\frac{36}{4}x + \frac{72}{4}y = -9x + 18y \]
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Now combine the results from both distributions:
\[ 4x - 4y - 9x + 18y \]
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Combine like terms:
\[ (4x - 9x) + (-4y + 18y) = -5x + 14y \]
Thus, the simplified expression is:
\[ -5x + 14y \]