Solve. Check your solution. \[ x-\frac{1}{5}=\frac{9}{5} \] The solution is \( \square \). (Type an integer or a fraction.)

To solve for \( x \), start by adding \( \frac{1}{5} \) to both sides of the equation: \[ x = \frac{9}{5} + \frac{1}{5} \] Combine the fractions: \[ x = \frac{9 + 1}{5} = \frac{10}{5} = 2 \] So, the solution is \( 2 \). To check the solution, substitute \( x = 2 \) back into the original equation: \[ 2 - \frac{1}{5} = \frac{9}{5} \] Calculating the left side gives: \[ 2 = \frac{10}{5} \Rightarrow \frac{10}{5} - \frac{1}{5} = \frac{9}{5} \] Since both sides are equal, the solution is verified!