What is the solution of the equation 2/5x+4=1/5

?(1 point)
Responses

−2/19
negative Start Fraction 2 over 19 End Fraction

−19/2
negative Start Fraction 19 over 2 End Fraction

21/2
Start Fraction 21 over 2 End Fraction

−38/25

1 answer

To solve the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \), follow these steps:

  1. Isolate the term with \( x \): \[ \frac{2}{5}x + 4 = \frac{1}{5} \] Subtract 4 from both sides: \[ \frac{2}{5}x = \frac{1}{5} - 4 \]

  2. 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: \[ \frac{2}{5}x = \frac{1 - 20}{5} = \frac{-19}{5} \]

  3. Next, multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \): \[ x = \left(\frac{-19}{5}\right) \cdot \left(\frac{5}{2}\right) \]

  4. The \( 5 \) in the numerator and denominator cancels out: \[ x = \frac{-19}{2} \]

Thus, the solution to the equation is: \[ \boxed{-\frac{19}{2}} \]