Literal Equations
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Equations with several variables (letters) are called literal equations. 

Your job, usually, will be to solve the equation for one of the variables.  The letters that do not represent your desired variable move to the other side of the equal sign so that the one variable you are solving for stands alone. 

Even though there are more letters in these equations, the methods used to solve these equations are the same as the methods you use to solve all equations.

Example #1 

 Steps 
Solve for x:  
ax + b = c
     - b   -b 

 

 1. Move b
(the opposite of add is subtract)
ax = c - b

 

 2. Move a
(the opposite of  multiply is divide)
 

3. x is what we are solving for and it stands alone.  Done.



Example #2 

 Steps 
Solve for h:  
A = ½ b h

     

 

 1. Move b by division
2.  Move the ½ by multiplying by the reciprocal (2/1)
 

3. h is what we are solving for and it stands alone.  Done.




Application Problem

Brandon knows that his truck route from Illinois to Tennessee is 430 miles long.
He also knows that Distance = rate • time (D = rt)
How long will his route take if he averages a speed of 50 mi/hr? 
Start by first solving the formula for time.

Solution: Steps:
solve for t (time)
 
substitute 430 in for D and 50 in for r and solve.
It will take Brandon 8.6 hours.


 

Application Problem

Shoe sizes and foot length are related by the formula 
S = 3F - 24,
 where S represents the shoe size
 and F represents the length of the foot, in inches.

Solve the formula for F.

Solution:

 Steps:
S = 3F - 24

 

 add 24 to both sides
S + 24 = 3F

 

 divide both sides by 3 

 

 simplify
Done.