Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 126

Solve $5n+3 = 2n+1$ and check.


$
\begin{equation}
\begin{aligned}

5n+3 =& 2n+1
&& \text{Given equation}
\\
\\
5n-2n =& 1-3
&& \text{Subtract $2n$ and subtract $3$ to each side}
\\
\\
3n =& -2
&& \text{Simplify}
\\
\\
\frac{\cancel{3}n}{\cancel{3}} =& \frac{-2}{3}
&& \text{Divide by } 3
\\
\\
n =& \frac{-2}{3}
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

5 \left( \frac{-2}{3} \right) + 3 =& 2 \left( \frac{-2}{3} \right) + 1
&& \text{Substitute } n = \frac{-2}{3}
\\
\\
\frac{-10}{3} + 3 =& \frac{-4}{3} + 1
&& \text{Simplify}
\\
\\
\frac{-1}{3} =& \frac{-1}{3}
&&

\end{aligned}
\end{equation}
$