To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), we first isolate \( x \).
- Subtract 4 from both sides:
\[ \frac{2}{5}x = \frac{1}{5} - 4 \]
To subtract 4, we can express it as a fraction with the same denominator:
\[ 4 = \frac{20}{5} \]
Therefore,
\[ \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5} \]
Now, we have:
\[ \frac{2}{5}x = \frac{-19}{5} \]
- Multiply both sides by \( \frac{5}{2} \) to solve for \( x \):
\[ x = \frac{-19}{5} \cdot \frac{5}{2} = \frac{-19 \cdot 5}{5 \cdot 2} = \frac{-19}{2} \]
So, the solution to the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \) is:
\[ \boxed{\frac{-19}{2}} \]
This corresponds to the response:
−19/2.