To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), follow these steps:
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Subtract 4 from both sides: \[ \frac{2}{5}x = \frac{1}{5} - 4 \]
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To perform the subtraction, convert 4 to a fraction with a common denominator: \[ 4 = \frac{20}{5} \] Therefore, \[ \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5} \] Now we have: \[ \frac{2}{5}x = \frac{-19}{5} \]
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To isolate \( x \), multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \): \[ x = \frac{-19}{5} \cdot \frac{5}{2} \]
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Simplify the right side: \[ x = \frac{-19 \cdot 5}{5 \cdot 2} = \frac{-19}{2} \]
Thus, the solution is: \[ \boxed{-\frac{19}{2}} \]