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 $\displaystyle n + \frac{2}{5} = \frac{2}{3}$