To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), follow these steps:
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Isolate the term with \( x \): \[ \frac{2}{5}x + 4 = \frac{1}{5} \] Subtract 4 from both sides: \[ \frac{2}{5}x = \frac{1}{5} - 4 \]
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To combine the numbers on the right side, convert 4 to a fraction with a denominator of 5: \[ 4 = \frac{20}{5} \] Now rewrite the equation: \[ \frac{2}{5}x = \frac{1}{5} - \frac{20}{5} \] This simplifies to: \[ \frac{2}{5}x = \frac{1 - 20}{5} = \frac{-19}{5} \]
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Next, multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \): \[ x = \left(\frac{-19}{5}\right) \cdot \left(\frac{5}{2}\right) \]
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The \( 5 \) in the numerator and denominator cancels out: \[ x = \frac{-19}{2} \]
Thus, the solution to the equation is: \[ \boxed{-\frac{19}{2}} \]