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 $\displaystyle \frac{5}{9} = b - \frac{1}{3}$