Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 56

Evaluate the equation $\displaystyle \frac{8x}{3} - \frac{x}{2} = -13$ and check your solution.


$
\begin{equation}
\begin{aligned}

\frac{8x}{3} - \frac{x}{2} =& -13
&& \text{Given equation}
\\
\\
6 \left( \frac{8x}{3} - \frac{x}{2} \right) =& (-13)(6)
&& \text{Multiply each side by the LCD, } 6
\\
\\
16 x - 3x =& -78
&& \text{Distributive property}
\\
\\
13x =& -78
&& \text{Combine like terms}
\\
\\
\frac{13x}{13} =& \frac{-78}{13}
&& \text{Divide both sides by $13$}
\\
\\
x =& -6
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

\frac{8(-6)}{3} - \left( \frac{-6}{2} \right) =& -13
&& \text{Let } x = -6
\\
-16 + 3 =& -13
&& \text{Simplify}
\\
-13 =& -13
&& \text{True}

\end{aligned}
\end{equation}
$