To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), follow these steps:
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Isolate the term with \( x \): Subtract 4 from both sides: \[ \frac{2}{5}x = \frac{1}{5} - 4 \]
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Convert 4 to a fraction with a denominator of 5: \[ 4 = \frac{20}{5} \] Therefore, we have: \[ \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5} \]
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Now the equation is: \[ \frac{2}{5}x = \frac{-19}{5} \]
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Multiply both sides by \(\frac{5}{2}\) to solve for \( x \): \[ x = \frac{-19}{5} \cdot \frac{5}{2} \]
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Simplifying: \[ x = \frac{-19 \cdot 5}{5 \cdot 2} = \frac{-19}{2} \]
The solution to the equation is: \[ \boxed{-\frac{19}{2}} \]