Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 74

Solve the equation $\displaystyle -\frac{1}{4} = c - \frac{2}{3}$ and check
if your answer is correct.

$
\begin{equation}
\begin{aligned}
-\frac{1}{4} + \frac{2}{3} &= c - \frac{2}{3} + \frac{2}{3} && \text{Add $\displaystyle \frac{2}{3}$ from each side} \\
\\
\frac{(-1)(3) + 2(4) }{12} &= c && \text{Get LCD}\\
\\
\frac{-3 + 8}{12} &= c\\
\\
\frac{5}{12} &= c
\end{aligned}
\end{equation}
$

By checking,

$
\begin{equation}
\begin{aligned}
-\frac{1}{4} &= \frac{5}{12} - \frac{2}{3} && \text{Replace the variable by the given number, } \frac{5}{12}\\
\\
\frac{-1}{4} &= \frac{5- 2(4)}{12} && \text{Evaluate the numerical expressions, then get the LCD}\\
\\
\frac{-1}{4} &= \frac{5-8}{12}\\
\\
\frac{-1}{4} &= \frac{-3}{12} && \text{Divide the right side of the equation by } 3\\
\\
-\frac{1}{4} &= - \frac{1}{4} && \text{Compare the results}
\end{aligned}
\end{equation}
$


The results are same; Therefore, $\displaystyle \frac{5}{12}$ is a solution of the equation $\displaystyle -\frac{1}{4} = c - \frac{2}{3}$