###### Example3.3.9

Solve for $$F$$ in $$C=\frac{5}{9}(F-32)\text{.}$$ (This represents the relationship between temperature in degrees Celsius and degrees Fahrenheit.)

To solve for $$F\text{,}$$ we first need to see that it is contained inside a set of parentheses. To get the expression $$F-32$$ on its own, we'll need to eliminate the $$\frac{5}{9}$$ outside those parentheses. One way we can “undo” this multiplication is by dividing each side by $$\frac{5}{9}\text{.}$$ As we learned in Section 3.2 though, a better approach is to instead multiply each side by the reciprocal of $$\frac{9}{5}\text{:}$$

\begin{align*} C\amp=\frac{5}{9}(\attention{F}-32)\\ \multiplyleft{\frac{9}{5}}C\amp=\multiplyleft{\frac{9}{5}}\frac{5}{9}(\attention{F}-32)\\ \frac{9}{5}C\amp=\attention{F}-32 \end{align*}

Now that we have $$F-32\text{,}$$ we simply need to add $$32$$ to each side to finish solving for $$F\text{:}$$