Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 64

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

$\begin{equation} \begin{aligned} c + \frac{3}{4} - \frac{3}{4} &= -\frac{1}{4} - \frac{3}{4} && \text{Subtract $\displaystyle \frac{3}{4}$ from each side} \\ \\ c &= -\frac{4}{4}\\ \\ c &= -1 \end{aligned} \end{equation}$

By checking,

$\begin{equation} \begin{aligned} - 1 + \frac{3}{4} &= \frac{-1}{4} && \text{Replace the variable by the given number, } -1\\ \\ \frac{-4 + 3}{4} &= \frac{-1}{4} && \text{Evaluate the numerical expressions}\\ \\ -\frac{1}{4} &= -\frac{1}{4} && \text{Compare the results} \end{aligned} \end{equation}$


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