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:


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