Math Help for Section 3.4, Page 133

Example
7: Tip

The proportion

    $\displaystyle{x\text{ dollars} \over
{58\text{ dollars}}} = {{2450\text{ miles}} \over {424\text{ miles}}}$

can be used because the units are the same on each side of the
proportion.

Study
Tip
To solve an equation, you want to isolate the variable. In Example 7,
multiplying each side by 58 was the only step needed to isolate the
variable.
However, cross-multiplication is also a valid way to solve
the equation.

Example
7: Check

   $\eqalign{ {x \over {58}} =&
{{2450} \over
{424}}&{\small\color{red}\quad\quad\text{Write original
quation.}} \cr {{\color{red}335.14} \over {58}}
\overset{?}{=}& {{2450} \over
{424}}&{\small\color{red}\quad\quad\text{Substitute 335.14
for }x.} \cr 5.77828… \approx&
5.77830…&{\small\color{red}\quad\quad\text{Solution checks. }
\checkmark} \cr} $

The answer does not check exactly in the original statement of the
problem because it is an approximation. However, the process of
checking solutions is still important.