Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 68

Solve the equation $\displaystyle \frac{4}{9} + a = -\frac{2}{9}$ and check
if your answer is correct.

$\begin{equation} \begin{aligned} \frac{4}{9} + a &= -\frac{2}{9} - \frac{4}{9} && \text{Subtract $\displaystyle \frac{4}{9}$ from each side} \\ \\ a &= \frac{-6}{9} && \text{Simplify}\\ \\ a &= -\frac{2}{3} && \text{Divide both sides by 3} \end{aligned} \end{equation}$

By checking,

$\begin{equation} \begin{aligned} \frac{4}{9} + \left( - \frac{2}{3} \right) &= - \frac{2}{9}&& \text{Replace the variable by the given number, } \frac{-2}{3}\\ \\ \frac{4-2(3)}{9} &= \frac{-2}{9} && \text{Evaluate the numerical expressions}\\ \\ \frac{-2}{9} &= -\frac{-2}{9} && \text{Compare the results} \end{aligned} \end{equation}$


The results are same; Therefore, $\displaystyle -\frac{2}{3}$ is a solution of the equation $\displaystyle \frac{4}{9} + a = -\frac{2}{9}$