Intermediate Algebra, Chapter 2, 2.2, Section 2.2, Problem 12

Solve $\displaystyle C = \frac{5}{9} (F - 32)$ for $F$.



$\begin{equation} \begin{aligned} C =& \frac{5}{9} (F - 32) && \text{Given equation} \\ \\ C =& \frac{5}{9} F - \frac{160}{9} && \text{Distributive property} \\ \\ C + \frac{160}{9} =& \frac{5}{9} F - \frac{160}{9} + \frac{160}{9} && \text{Add each side by } \frac{160}{9} \\ \\ C + \frac{160}{9} =& \frac{5}{9} F && \text{Combine like terms} \\ \\ \frac{9}{5} \left( C + \frac{160}{9} \right) =& \frac{9}{5} \left( \frac{5}{9} F \right) && \text{Multiply each side by } \frac{9}{5} \\ \\ \frac{9}{5}C + 32 =& F && \text{Solve for $F$} \\ \text{ or } & && \\ \\ F =& \frac{9}{5}C + 32 && \end{aligned} \end{equation}$