To simplify the expression \( \frac{2}{5}(10x - 10y) - \frac{3}{4}(12x - 24y) \), let's break it down step by step.
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Distribute the fractions: \[ \frac{2}{5}(10x - 10y) = \frac{2 \cdot 10x}{5} - \frac{2 \cdot 10y}{5} = \frac{20x}{5} - \frac{20y}{5} = 4x - 4y \] \[ -\frac{3}{4}(12x - 24y) = -\left(\frac{3 \cdot 12x}{4} - \frac{3 \cdot 24y}{4}\right) = -\left(9x - 18y\right) = -9x + 18y \]
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Combine both results: Now, we add the results: \[ (4x - 4y) + (-9x + 18y) = 4x - 9x - 4y + 18y \] \[ = (4x - 9x) + (-4y + 18y) = -5x + 14y \]
Thus, the simplified expression is: \[ -5x + 14y \]
If you have multiple-choice options and need to check which option is equivalent to \( -5x + 14y \), you can compare the expressions to find the equivalent one.
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