3.6  Literal Equations and Formulas

Mrs. Agriesti's Algebra

Goal:  To learn to solve formulas for a specified variable.


Literal Equation--an equation that has more than one variable.  Ex:  The formula for the perimeter of a rectangle - P = 2L+2W

Solve for--get it by itself.

Example 1:     Solve P = 2W + 2L for the length L.

First, Locate the term with the variable in it that you want to solve for (2L).  Do the opposite of whatever is on the same side as that  term (Subtract 2W).  Remember, you cannot combine two terms that are not 'like terms'. 

After the term with the variable is isolated, divide or multiply by the reciprocal to isolate the variable itself (Divide by 2).

Simplify, and rewrite the equation with the variable on the left if necessary.

Example 2:     Solve A= ½ h (b₁ + b₂) for the height h.

First, find h.  Notice that it is being multiplied by a fraction.  Multiply by the reciprocal to get rid of the fraction. 




We don't distribute this time, instead divide both sides by the quantity in the parenthesis. 


Simplify and h is now isolated.





Rewrite with the variable on the left side.

Example 3:     Solve A = P + Prt for the interest rate r.

First, Locate the term with the variable in it that you want to solve for (r).  Do the opposite of whatever is on the same side as that  term (Subtract P).  Remember, you cannot combine two terms that are not 'like terms'. 

After the term with the variable is isolated, divide to isolate r (Divide by P and t).

Simplify, and rewrite the equation with the variable on the left if necessary.

Hint:  Look also at the examples in the book.  Example 3 will help you with problem #9 and #10.