Solving Literal Equations
Literal Equations – Equations with multiple variables where you are asked to solve for just one
of the variables. (Usually represent formulas used in the sciences and/or geometry)
To solve literal equations: Use the same process you use to isolate the variable in an algebraic
equation with one variable. It’s just that you are going to be adding, subtracting, multiplying,
and dividing (and sometimes factoring) variables as well as numbers.
CAUTION: BE CAREFUL NOT TO COMBINE UNLIKE TERMS!
Example 1:
Solve .
Goal: Isolate R to get R = an expression in E and I
To isolate R, divide both sides of the equation by I:
Simplify:
Solution: Example 2:
Solve
.
Goal: Isolate t to get t = an expression in d and r
First multiply both sides of the equation by t to clear the fractions:
Simplify:
To isolate t, divide both sides of the equation by r:
Simplify:
Solution: Example 3:
Solve Goal: Isolate b1 to get b1 = an expression in A, h, & b2 (Note: b1 and b2 are two different variables.)
First multiply both sides of the equation by 2 to clear the fractions:
2 2 (continued on next page)
Simplify:
2 Distribute h:
2 Next subtract hb2 from both sides of the equation to get hb1 alone:
2 2 To isolate b1, divide both sides of the equation by h:
!
Simplify:
2 Solution: Example 4:
"#
Solve #$ %
Goal: Isolate N to get N = an expression in I, P, R, & A:
First multiply both sides of the equation by (RN+A) to clear the fractions:
"#
% % #$
Simplify:
% &%
Distribute I:
% &%
Subtract IRN from both sides to get all N’s on the same side:
% &%
%
%
Note: PN & IRN are not like terms we cannot combine them!
&% %
But we can factor out the N from each term!
%& Finally, we can divide both sides by (P – IR) to isolate N:
#"
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Simplify:
%
& Solution: % &
Practice Problems
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