Question

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

Answer 1

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

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

2. **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:
\[
\boxed{\frac{-19}{2}}
\]