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 $\displaystyle x - \frac{2}{5} = \frac{3}{5}$