To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), follow these steps:
-
Isolate the \( x \) term: Subtract 4 from both sides: \[ \frac{2}{5}x + 4 - 4 = \frac{1}{5} - 4 \] This simplifies to: \[ \frac{2}{5}x = \frac{1}{5} - 4 \]
-
Convert 4 to a fraction with a common denominator: Since 4 can be expressed as \( \frac{20}{5} \): \[ \frac{2}{5}x = \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5} \]
-
Solve for \( x \): Multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \): \[ x = \frac{-19}{5} \times \frac{5}{2} \]
-
Simplify: \[ x = \frac{-19 \cdot 5}{5 \cdot 2} = \frac{-19}{2} \]
Thus, the solution to the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \) is \[ \boxed{-\frac{19}{2}} \]