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 $\displaystyle \frac{4}{9} + a = -\frac{2}{9}$