Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 58

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


$
\begin{equation}
\begin{aligned}

\frac{2x - 3}{7} + \frac{3}{7} =& - \frac{x}{3}
&& \text{Given equation}
\\
3 (2x - 3 + 3) =& -7x
&& \text{Multiply each side by the LCD } 21
\\
3(2x) =& -7x
&& \text{Combine like terms}
\\
6x =& -7x
&& \text{Distributive property}
\\
6x + 7x =& 0
&& \text{Add $7x$ from each side}
\\
13x =& 0
&& \text{Combine like terms}
\\
\frac{13x}{13} =& \frac{0}{13}
&& \text{Divide both sides by $13$}
\\
x =& 0
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

\frac{2(0) - 3}{7} + \frac{3}{7} =& - \frac{0}{3}
&& \text{Let } x = 0
\\
\\
- \frac{3}{7} + \frac{3}{7} =& - \frac{0}{3}
&& \text{Multiply}
\\
\\
0 =& 0
&& \text{True}

\end{aligned}
\end{equation}
$