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}
$