To solve the inequality \( -\frac{1}{5}x - 16 > 32 \frac{2}{5} \), we first need to convert the mixed number \( 32 \frac{2}{5} \) to an improper fraction.
- Convert \( 32 \frac{2}{5} \) to an improper fraction: \[ 32 \frac{2}{5} = 32 + \frac{2}{5} = \frac{160}{5} + \frac{2}{5} = \frac{162}{5} \]
Now the inequality becomes: \[ -\frac{1}{5}x - 16 > \frac{162}{5} \]
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Next, we add 16 to both sides. First, convert 16 to a fraction with a denominator of 5: \[ 16 = \frac{80}{5} \] So the inequality now is: \[ -\frac{1}{5}x > \frac{162}{5} + \frac{80}{5} \] \[ -\frac{1}{5}x > \frac{242}{5} \]
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Now multiply both sides of the inequality by -5. Remember that when you multiply or divide by a negative number, you must flip the inequality sign: \[ x < -242 \]
Thus, the solution to the inequality is: \[ x < -242 \]