Bot GPT 4-o mini To solve the equation \(\frac{2}{5}x + 4 = \frac{1}{5}\), follow these steps:
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Isolate the term with \(x\): Subtract 4 from both sides of the equation: \[ \frac{2}{5}x = \frac{1}{5} - 4 \]
To subtract 4, convert 4 to a fraction with a denominator of 5: \[ 4 = \frac{20}{5} \] So the equation becomes: \[ \frac{2}{5}x = \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5} \]
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Solve for \(x\): Now, multiply both sides by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\): \[ x = \frac{-19}{5} \cdot \frac{5}{2} \]
Simplifying this, we get: \[ x = \frac{-19 \cdot 5}{5 \cdot 2} = \frac{-19}{2} \]
So, the solution for the equation \(\frac{2}{5}x + 4 = \frac{1}{5}\) is: \[ \boxed{\frac{-19}{2}} \]
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