Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 54

Evaluate the equation $\displaystyle \frac{x}{5} - \frac{x}{4} = 1$ and check your solution.


$
\begin{equation}
\begin{aligned}

\frac{x}{5} - \frac{x}{4} =& 1
&& \text{Given equation}
\\
\\
20 \left( \frac{x}{5} - \frac{x}{4} \right) =& 1(20)
&& \text{Multiply each side by } 20
\\
\\
4x - 5x =& 20
&& \text{Distributive property}
\\
\\
-x =& 20
&& \text{Combine like terms}
\\
\\
x =& -20
&& \text{Divide both sides by $-1$}


\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

\frac{-20}{5} - \left( \frac{-20}{4} \right) =& 1
&& \text{Let } x = -20
\\
\\
-4 + 5 =& 1
&& \text{Simplify}
\\
\\
1 =& 1
&& \text{True}

\end{aligned}
\end{equation}
$