x-0.2x=8/15

To solve the equation \( x - 0.2x = \frac{8}{15} \), we can start by simplifying the left side of the equation.

1. Combine like terms: \[ x - 0.2x = 0.8x \] So the equation becomes: \[ 0.8x = \frac{8}{15} \]

2. Now, to solve for \( x \), divide both sides by \( 0.8 \): \[ x = \frac{8/15}{0.8} \]

3. We can rewrite \( 0.8 \) as a fraction: \[ 0.8 = \frac{8}{10} = \frac{4}{5} \] Therefore, we can write: \[ x = \frac{8/15}{4/5} \]

4. Dividing by a fraction is equivalent to multiplying by its reciprocal: \[ x = \frac{8}{15} \times \frac{5}{4} \]

5. Now multiply the fractions: \[ x = \frac{8 \cdot 5}{15 \cdot 4} \] \[ = \frac{40}{60} \]

6. Simplifying \( \frac{40}{60} \): \[ = \frac{2}{3} \]

Therefore, the solution to the equation \( x - 0.2x = \frac{8}{15} \) is: \[ \boxed{\frac{2}{3}} \]