To solve the inequality \( \frac{1}{5} - 16 > 32 \frac{2}{5} \), we first need to express all numbers in a common format.
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Convert \( 32 \frac{2}{5} \) to an improper fraction: \[ 32 \frac{2}{5} = 32 + \frac{2}{5} = \frac{32 \times 5}{5} + \frac{2}{5} = \frac{160 + 2}{5} = \frac{162}{5} \]
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Now, rewrite the inequality: \[ \frac{1}{5} - 16 > \frac{162}{5} \]
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Convert \( -16 \) to a fraction with the same denominator: \[ -16 = \frac{-80}{5} \]
Now substitute this back into the inequality: \[ \frac{1}{5} - \frac{80}{5} > \frac{162}{5} \]
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Combine the fractions on the left side: \[ \frac{1 - 80}{5} > \frac{162}{5} \] \[ \frac{-79}{5} > \frac{162}{5} \]
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To simplify this inequality, we can multiply through by 5 (since 5 is positive, the direction of the inequality stays the same): \[ -79 > 162 \]
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This is not true, as \(-79\) is not greater than \(162\).
Thus, the original inequality \( \frac{1}{5} - 16 > 32 \frac{2}{5} \) is false.