8. \( \left(\frac{2}{5} x+\frac{1}{5}\right)-\frac{3}{10} \)

To simplify the expression \( \left(\frac{2}{5} x+\frac{1}{5}\right)-\frac{3}{10} \), start by finding a common denominator for the fractions involved. The common denominator for \( \frac{5}{5} \) and \( \frac{10}{10} \) is \( 10 \). Rewrite the expression: \( \frac{2}{5} = \frac{4}{10} \) and \( \frac{1}{5} = \frac{2}{10} \). Now, the expression becomes: \[ \left(\frac{4}{10} x + \frac{2}{10}\right) - \frac{3}{10} \] Combine the constants: \[ \frac{4}{10} x + \frac{2}{10} - \frac{3}{10} = \frac{4}{10} x + \frac{2 - 3}{10} = \frac{4}{10} x - \frac{1}{10} \] Thus, the simplified expression is: \[ \frac{4}{10} x - \frac{1}{10} \] or equivalently: \[ \frac{2}{5} x - \frac{1}{10} \] This gives you a cleaner form of the original expression!