Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 72

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

$
\begin{equation}
\begin{aligned}
n + \frac{2}{5}- \frac{2}{5} &= \frac{2}{3} - \frac{2}{5} && \text{Subtract $\displaystyle \frac{1}{6}$ from each side} \\
\\
n &= \frac{2(5) - 2(3)}{15} && \text{Get LCD}\\
\\
n &= \frac{10 - 6}{15}\\
\\
n &= \frac{4}{15}
\end{aligned}
\end{equation}
$

By checking,

$
\begin{equation}
\begin{aligned}
\frac{4}{15} + \frac{2}{5} &= \frac{2}{5} && \text{Replace the variable by the given number, } \frac{4}{15}\\
\\
\frac{4+2(3)}{15} &= \frac{2}{3} && \text{Evaluate the numerical expressions}\\
\\
\frac{4+6}{15} &= -\frac{2}{3}\\
\\
\frac{10}{15} &= \frac{2}{3}\\
\\
\frac{2}{3} &= \frac{2}{3} && \text{Compare the results}
\end{aligned}
\end{equation}
$


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