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 \( x \): Subtract 4 from both sides:
\[ \frac{2}{5} x + 4 - 4 = \frac{1}{5} - 4 \]
This simplifies to:
\[ \frac{2}{5} x = \frac{1}{5} - \frac{20}{5} \]
\[ \frac{2}{5} x = \frac{1 - 20}{5} \]
\[ \frac{2}{5} x = \frac{-19}{5} \]
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Solve for \( x \): Multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \):
\[ x = \frac{-19}{5} \cdot \frac{5}{2} \]
Simplifying:
\[ x = \frac{-19 \cdot 5}{5 \cdot 2} = \frac{-19}{2} \]
Thus, the solution is:
\[ x = -\frac{19}{2} \]
The correct response from your options is:
−192 (which is equivalent to negative Start Fraction 19 over 2 End Fraction).