To solve \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, we first convert the mixed numbers to improper fractions:
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For \(-24 \frac{4}{5}\): \[ -24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\left(120 + 4\right)/5 = -\frac{124}{5} \]
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For \(-6 \frac{7}{10}\): \[ -6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\left(60 + 7\right)/10 = -\frac{67}{10} \]
Now we need a common denominator to subtract these fractions. The least common multiple of 5 and 10 is 10.
We convert \(-\frac{124}{5}\) to have a denominator of 10: \[ -\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10} \]
Now we can perform the subtraction: \[ -\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10} \]
This simplifies to: \[ -\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2} \]
Thus, the result of \(-24 \frac{4}{5} - 6 \frac{7}{10}\) is \(-31 \frac{1}{2}\).
Therefore, the answer is: D. -31 1/2
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