To solve the inequality \( -\frac{1}{5} - 16 > 32 \frac{2}{5} \), we can first convert everything to improper fractions or decimals to make computations easier.
First, convert \( 32 \frac{2}{5} \) to an improper fraction:
\[ 32 \frac{2}{5} = 32 + \frac{2}{5} = \frac{32 \times 5}{5} + \frac{2}{5} = \frac{160 + 2}{5} = \frac{162}{5} \]
Next, rewrite \( -\frac{1}{5} - 16 \) as:
\[
- \frac{1}{5} - 16 = -\frac{1}{5} - \frac{16 \times 5}{5} = -\frac{1}{5} - \frac{80}{5} = -\frac{1 + 80}{5} = -\frac{81}{5} \]
Now, we can rewrite the inequality:
\[ -\frac{81}{5} > \frac{162}{5} \]
To eliminate the fractions, multiply through by \( 5 \) (noting that this doesn't change the direction of the inequality since \( 5 \) is positive):
\[ -81 > 162 \]
This statement is false. Thus, the original inequality \( -\frac{1}{5} - 16 > 32 \frac{2}{5} \) is also false.
Final answer: The inequality does not hold.