Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 60

Evaluate the equation $\displaystyle \frac{3x + 2}{7} - \frac{x + 4}{5} = 2$ and check your solution.


$
\begin{equation}
\begin{aligned}

\frac{3x + 2}{7} - \frac{x + 4}{5} =& 2
&& \text{Given equation}
\\
\\
35 \left( \frac{3x + 2}{7} - \frac{x + 4}{5} \right) =& 2(35)
&& \text{Multiply each side by the LCD } 35
\\
\\
15x + 10 - 7x - 28 =& 70
&& \text{Distributive property}
\\
\\
8x - 18 =& 70
&& \text{Combine like terms}
\\
\\
8x =& 70 + 18
&& \text{Add $18$ from each side}
\\
\\
8x =& 88
&& \text{Combine like terms}
\\
\\
\frac{8x}{8} =& \frac{88}{8}
&& \text{Divide both sides by $8$}
\\
\\
x =& 11
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

\frac{3(11) + 2}{7} - \frac{11 + 4}{5} =& 2
&& \text{Let } x = 11
\\
\\
\frac{33 + 2}{7} - \frac{11 + 4}{5} =& 2
&& \text{Multiply}
\\
\\
5 - 3 =& 2
&& \text{Simplify}
\\
\\
2 =& 2
&& \text{True}

\end{aligned}
\end{equation}
$