Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 66

Solve the equation $\displaystyle x - \frac{2}{5} = \frac{3}{5}$ and check
if your answer is correct.

$\begin{equation} \begin{aligned} x - \frac{2}{5} + \frac{2}{5} &= \frac{3}{5} + \frac{2}{5} && \text{Add $\displaystyle \frac{2}{4}$ from each side} \\ \\ x &= \frac{5}{5}\\ \\ x &= 1 \end{aligned} \end{equation}$

By checking,

$\begin{equation} \begin{aligned} 1 - \frac{2}{5} &= \frac{3}{5} && \text{Replace the variable by the given number, } 1\\ \\ \frac{5-2}{5} &= \frac{3}{5} && \text{Evaluate the numerical expressions}\\ \\ \frac{3}{5} &= \frac{3}{5} && \text{Compare the results} \end{aligned} \end{equation}$

The results are same; Therefore, $1$ is a solution of the equation $\displaystyle x - \frac{2}{5} = \frac{3}{5}$