To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), we can follow these steps:
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Subtract 4 from both sides: \[ \frac{2}{5}x + 4 - 4 = \frac{1}{5} - 4 \] Simplifying the right side: \[ \frac{1}{5} - 4 = \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5} \] So the equation now is: \[ \frac{2}{5}x = \frac{-19}{5} \]
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Multiply both sides by \( \frac{5}{2} \) to solve for \( x \): \[ x = \frac{-19}{5} \cdot \frac{5}{2} \] The \( 5 \) cancels out: \[ x = \frac{-19}{2} \]
Thus, the solution to the equation is: \[ x = -\frac{19}{2} \]
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