To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), we can 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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Convert 4 to a fraction with a denominator of 5: \[ 4 = \frac{20}{5} \] So we have: \[ \frac{2}{5}x = \frac{1}{5} - \frac{20}{5} \] This simplifies to: \[ \frac{2}{5}x = \frac{1 - 20}{5} = \frac{-19}{5} \]
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Solve for \( x \): To solve for \( x \), multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \): \[ x = \frac{-19}{5} \cdot \frac{5}{2} \] The \( 5 \)s cancel out: \[ x = \frac{-19}{2} \]
So the solution is: \[ x = -\frac{19}{2} \]
The corresponding answer from the choices provided is: −192 (negative Start Fraction 19 over 2 End Fraction).
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