Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 66

Evaluate the equation $\displaystyle 0.20(14,000) + 0.14x = 0.18(14,000 + x)$ and check your solution.


$
\begin{equation}
\begin{aligned}

0.20(14,000) + 0.14x =& 0.18(14,000 + x)
&& \text{Given equation}
\\
100 [0.20(14,000) + 0.14x] =& 100 [0.18 (14,000 + x)]
&& \text{Multiply each term by $100$}
\\
20(14,000) + 14x =& 18(14,000 + x)
&& \text{Distributive property}
\\
280,000 + 14x =& 252,000 + 18x
&& \text{Distributive property}
\\
14x - 18x =& 252,000 - 280,000
&& \text{Subtract $(18x+ 280,000)$ from each side}
\\
-4x =& -28,000
&& \text{Combine like terms}
\\
\frac{-4x}{-4} =& \frac{-28,000}{-4}
&& \text{Divide both sides by $-4$}
\\
x =& 7,000
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

0.20(14,000) + 0.14(7,000) =& 0.18(14,000 + 7,000)
&& \text{Let } x = 7,000
\\
2,800 + 980 =& 3,780
&& \text{Multiply}
\\
3,780 =& 3,780
&& \text{True}

\end{aligned}
\end{equation}
$