7. Formulas and Literal Equations

A formula is an equation with more than one variable. A literal equation asks you to solve for one variable in terms of the others.

The same rules apply: isolate the target variable.

Example 1 - rectangle area:
\[ A = lw. \]
Solve for \(w\). Since \(w\) is multiplied by \(l\), divide both sides by \(l\):
\[ w = \frac{A}{l}. \]

Example 2 - distance:
\[ d = rt. \]
Solve for \(t\):
\[ t = \frac{d}{r}. \]

Example 3 - perimeter of a rectangle:
\[ P = 2l + 2w. \]
Solve for \(l\). Subtract \(2w\):
\[ P - 2w = 2l. \]
Divide by 2:
\[ l = \frac{P - 2w}{2}. \]

Example 4 - line equation:
\[ y = 3x + 2. \]
If \(y=20\), solve \(20=3x+2\):
\[ 18=3x,\qquad x=6. \]

Common mistake: dividing only one term by 2 in \(P-2w=2l\). The whole expression \(P-2w\) is divided by 2.