Practice Solving Literal Equations

Formulas may contain multiple variables, along with known numbers and letters that stand for known constants like ‍\(\pi\).

We can highlight a certain variable in the formula by treating the formula as an equation where we want to solve for that variable.

1. In this case, we need to solve the equation \(F=\frac{9}{5}C+32\) for C.

   \(F=\frac{9}{5}C+32\)

   \(F-32=\frac{9}{5}C\)

   \(\frac{5}{9} \cdot (F-32)\)
   

   This is the result of rearranging the formula to highlight the measure in degrees Celsius:

   \(C=\frac{5}{9} \cdot (F-32)\)

2. In this case, we need to solve the equation \(U=\frac{W}{O}\) for O.

   \(U=\frac{W}{O}\)

   \(U \cdot =W\)

   \(O=\frac{W}{U}\)

   This is the result of rearranging the formula to highlight the hourly output per worker:
   

   \(O=\frac{W}{U}\)

3. In this case, we need to solve the equation

   \(A=\frac{1}{2}(b+c)h\) for h.

   \(A=\frac{1}{2}(b+c)h\)

   \(\frac{2A}{b+c}=h\)

   This is the result of rearranging the formula to highlight the height:

   \(h=\frac{2A}{b+c}\)

4. In this case, we need to solve the equation \(S = \frac{D}{T}\) for T.

   \(S = \frac{D}{T}\)

   \(S \cdot T = D\)

   \(T = \frac{D}{S}\)

   This is the result of rearranging the formula to highlight time:

   \(T = \frac{D}{S}\)