Question

What is the solution of the equation 2/5x+4=1/5?(1 point)
Responses

−219
negative Start Fraction 2 over 19 End Fraction

212
Start Fraction 21 over 2 End Fraction

−3825
negative Start Fraction 38 over 25 End Fraction

−192
negative Start Fraction 19 over 2 End Fraction

Answer 1

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

1. **Isolate the term with \( x \)**:
\[
\frac{2}{5}x + 4 - 4 = \frac{1}{5} - 4
\]
This simplifies to:
\[
\frac{2}{5}x = \frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5}
\]

2. **Multiply both sides by the reciprocal of \( \frac{2}{5} \)**, which is \( \frac{5}{2} \):
\[
x = \frac{-19}{5} \cdot \frac{5}{2}
\]
The \( 5 \) in the numerator and denominator cancels out:
\[
x = \frac{-19}{2}
\]

The solution is:
\[
x = -\frac{19}{2}
\]

Thus, the correct response is:
\[
\text{negative Start Fraction 19 over 2 End Fraction}
\]