To multiply the expressions \( \frac{4}{5}x \) and \( -\frac{3}{4} \), we follow these steps:
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Multiply the coefficients: \[ \frac{4}{5} \times -\frac{3}{4} = \frac{4 \times -3}{5 \times 4} = \frac{-12}{20} \]
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Simplify \( \frac{-12}{20} \): \[ \frac{-12}{20} = \frac{-3}{5} \quad \text{(dividing numerator and denominator by 4)} \]
Therefore, the result of multiplying \( \frac{4}{5}x \) by \( -\frac{3}{4} \) is:
\(-\frac{3}{5}x\).
From the choices given, the correct answer for the coefficient is:
B: -3/5.