To evaluate the expression \( \frac{3(6 - 14)}{-4} \), we will follow the steps below:
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Calculate the expression in the parentheses: \[ 6 - 14 = -8 \]
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Substitute the result back into the expression: \[ \frac{3(-8)}{-4} \]
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Multiply the numbers in the numerator: \[ 3 \times -8 = -24 \]
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Now the expression becomes: \[ \frac{-24}{-4} \]
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Divide -24 by -4: \[ \frac{-24}{-4} = 6 \]
Thus, the value of the expression is \( \boxed{6} \).