Question

2/5x+4=1/5

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:
\[
\frac{2}{5}x = \frac{1}{5} - 4
\]

To simplify \( \frac{1}{5} - 4 \), we need a common denominator:
\[
4 = \frac{20}{5}
\]
Therefore:
\[
\frac{1}{5} - \frac{20}{5} = \frac{1 - 20}{5} = \frac{-19}{5}
\]

Now the equation is:
\[
\frac{2}{5}x = \frac{-19}{5}
\]

2. **Solve for \( x \)**:
To isolate \( x \), multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \):
\[
x = \frac{-19}{5} \cdot \frac{5}{2}
\]

Simplifying:
\[
x = \frac{-19 \cdot 5}{5 \cdot 2} = \frac{-19}{2}
\]

So, the solution to the equation \( \frac{2}{5}x + 4 = \frac{1}{5} \) is:
\[
x = -\frac{19}{2}
\]