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