Solving Literal Equations - Tutorial

A literal equation is an equation that expresses a relationship between two or more variables. A formula is an example of a literal equation. We present a tutorial on how to solve literal equations for one of the variables. Detailed solutions to examples and answers to exercises are presented.

How to Solve Literal Equations? Examples with Detailed Solutions

Example 1

Solve the literal equation
P = 2L + 2W
for W.

Solution to Example 1


Example 2

Solve the literal equation
H = √ ( x 2 + y 2)

for y, where H, x and y are a positive real numbers and H is greater than x and greater than y.

Solution to Example 2


Example 3

Express F in terms of C in the literal equation
C = (5 / 9)(F - 32)
.

Solution to Example 3


Example 4

Express y in terms of x in the literal equation
a x + b y = c , with b not equal to zero.
.

Solution to Example 4

Exercises

Solve each of the literal equations below for the indicated variable.(see answers below).
  1. A = W L , for L.

  2. y = m x + b , for x.

  3. A = (1 / 2)(B + a) , for a.

  4. S = 2 π r h , for r.

  5. F = (9 / 5)C + 32 , for C.

  6. 1 / x = 1 / y + 1 / z , for y.

Answers to Above Exercises:


  1. L = A / W

  2. x = (y - b) / m , for m not equal to zero.

  3. a = 2 A - B

  4. r = S / (2 π h)

  5. C = (5 / 9)(F - 32)

  6. y = (x z) / (z - x) , for z not equal to x.

More References and links

Solve Equations, Systems of Equations and Inequalities.