Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 70

Evaluate the equation $\displaystyle 0.004x + 0.006(50 - x) = 0.004 (68)$ and check your solution.


$
\begin{equation}
\begin{aligned}

0.004x + 0.006(50 - x) =& 0.004 (68)
&& \text{Given equation}
\\
1000[0.004x + 0.006(50-x)] =& 1000 [0.004(68)]
&& \text{Multiply each term by $1000$}
\\
4x + 6(50-x) =& 4(68)
&& \text{Distributive property}
\\
4x + 300 -6x =& 272
&& \text{Distributive property}
\\
-2x + 300 =& 272
&& \text{Combine like terms}
\\
-2x =& 272 - 300
&& \text{Subtract $300$ from each side}
\\
-2x =& -28
&& \text{Combine like terms}
\\
\frac{-2x}{2} =& \frac{-28}{2}
&& \text{Divide both sides by $-2$}
\\
x =& 14
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

0.004(14) + 0.006(50-14) =& 0.004(68)
&& \text{Let } x = 14
\\
0.056 + 0.216 =& 0.272
&& \text{Multiply}
\\
0.272 =& 0.272
&& \text{True}

\end{aligned}
\end{equation}
$