Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 70

Solve the equation $\displaystyle b + \frac{1}{6} = -\frac{1}{3} $ and check
if your answer is correct.

$
\begin{equation}
\begin{aligned}
b + \frac{1}{6} - \frac{1}{6} &= -\frac{1}{3} - \frac{1}{6} && \text{Subtract $\displaystyle \frac{1}{6}$ from each side} \\
\\
b &= \frac{(-1)(2) - 1}{6} && \text{Get LCD}\\
\\
b &= \frac{-2-1}{6}\\
\\
b &= -\frac{3}{6}\\
\\
b &= - \frac{1}{2}
\end{aligned}
\end{equation}
$

By checking,

$
\begin{equation}
\begin{aligned}
-\frac{1}{2} + \frac{1}{6} &= - \frac{1}{3} && \text{Replace the variable by the given number, } \frac{-1}{2}\\
\\
\frac{(-1)(3) + 1}{6} &= -\frac{1}{3} && \text{Evaluate the numerical expressions}\\
\\
\frac{-3+1}{6} &= -\frac{1}{3}\\
\\
\frac{-2}{6} &= \frac{-1}{3}\\
\\
\frac{-1}{3} &= \frac{-1}{3} && \text{Compare the results}
\end{aligned}
\end{equation}
$


The results are same; Therefore, $\displaystyle -\frac{1}{2}$ is a solution of the equation $\displaystyle b + \frac{1}{6} = -\frac{1}{3}$