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 $\displaystyle -\frac{1}{4} = c - \frac{2}{3}$