6. Literal Equations and Rearranging Formulas

A literal equation asks you to solve for a variable while other letters remain in the answer. Treat the other letters like numbers.

Example 1:
\[ A=lw. \]
Solve for \(w\):
\[ w=\frac{A}{l}. \]

Example 2:
\[ P=2l+2w. \]
Solve for \(l\). Subtract \(2w\):
\[ P-2w=2l. \]
Divide by 2:
\[ l=\frac{P-2w}{2}. \]

Example 3:
\[ C=\frac{5}{9}(F-32). \]
Solve for \(F\). Multiply by \(\frac{9}{5}\):
\[ \frac{9}{5}C=F-32. \]
Add 32:
\[ F=\frac{9}{5}C+32. \]

Example 4:
\[ y=mx+b. \]
Solve for \(m\). Subtract \(b\):
\[ y-b=mx. \]
Divide by \(x\):
\[ m=\frac{y-b}{x}. \]

Common mistake: dividing only one term. In \(l=\frac{P-2w}{2}\), the entire numerator \(P-2w\) is divided by 2.