Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 76

Solve the equation $\displaystyle \frac{5}{9} = b - \frac{1}{3}$ and check
if your answer is correct.

$
\begin{equation}
\begin{aligned}
\frac{5}{9} + \frac{1}{3} &= b - \frac{1}{3} + \frac{1}{3} && \text{Add $\displaystyle \frac{1}{3}$ from each side} \\
\\
\frac{5 + 3 (3)}{9} &= b && \text{Take the LCD}\\
\\
\frac{5+9}{9} &= b\\
\\
\frac{14}{9} &= b
\end{aligned}
\end{equation}
$

By checking,

$
\begin{equation}
\begin{aligned}
\frac{5}{9} &= \frac{14}{9} - \frac{1}{3} && \text{Replace the variable by the given number, } \frac{14}{9}\\
\\
\frac{5}{9} &= \frac{14 -3(3)}{9} && \text{Evaluate the numerical expressions, then get the LCD}\\
\\
\frac{5}{9} &= \frac{14-9}{9}\\
\\
\frac{5}{9} &= \frac{5}{9} && \text{Compare the results}
\end{aligned}
\end{equation}
$


The results are same; Therefore, $\displaystyle \frac{14}{9}$ is a solution of the equation $\displaystyle \frac{5}{9} = b - \frac{1}{3}$