To solve the equation \( \frac{2}{5} x + 4 = \frac{1}{5} \), we can begin isolating \( x \).
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First, start with the equation: \[ \frac{2}{5} x + 4 = \frac{1}{5} \]
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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 \( 5 \): \[ 4 = \frac{20}{5} \] So we have: \[ \frac{2}{5} x = \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5} \]
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Now, multiply both sides by \( \frac{5}{2} \) to solve for \( x \): \[ x = \frac{-19}{5} \times \frac{5}{2} = \frac{-19}{2} \]
So, the solution for \( x \) is \( -\frac{19}{2} \).
The correct answer is C. \( -\frac{19}{2} \).
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