How to solve literal equations

Here, you will learn how to solve literal equations with some carefully chosen examples. What is a literal equation? It is an equation that has many variables and we need to solve for one of the variables. Study the one below carefully!

How to solve literal equations

The literal equation we just solved is ax = b.

y  = mx + b is also a literal equation. See below a more detailed guideline showing how to solve y = mx + b for x as we solve 8 = 2x + 4 for x. 

 y = mx + b

 Subtract b from both sides

 y - b = mx + b - b

 y - b = mx

 Divide both sides by m

 (y - b) / m   =   (m/m)x

 ( y - b) / m  = 1x

 (y - b) / m  = x

 8 = 2x + 4

 Subtract 4 from both sides

 8 - 4 = 2x + 4 - 4

 8 - 4 = 2x    

 Divide both sides by 2

 (8 - 4) / 2 = (2 / 2) x

 (8 - 4) / 2 = 1x

 (8 - 4) / 2 = x


We can see that the process is similar whether we are solving a literal equation or not.
All we need to do is to isolate things. For (8 - 4) / 2 = x though, we can take a step further by doing the math since we are dealing with numbers.

Therefore, x = (8 - 4) / 2 = 4 / 2 = 2

Hopefully, this example was clear enough to put you on the right track.  

More examples showing how to solve literal equations.

1)

Solve 2a + b = d for b

2a + b = d

We need to isolate b, therefore, get rid of  2a by subtracting 2a from both sides of the equation.

2a - 2a + b = d - 2a

0 + b  = d - 2a

      b   = d - 2a

2)

Solve V = lwh for w.

We need to get rid of lh. Rewrite the equation.

   V =  lhw

Get rid of lh by dividing both sides of the equation by lh

  V / lh   = (lh / lh)w

  V / lh  = 1w

  V / lh = w

3)

Solve x =
a + b + c / 3
  for c


Multiply both sides of the equation by 3

3 × x =
a + b + c / 3
×3


3x = a + b + c

We need to get rid of a and b.

Subtract a from both sides

3x  - a  = a - a + b + c

3x - a  = 0 + b + c

3x - a = b + c

Subtract b from both sides

3x - a - b = b - b + c

3x - a  - b = 0 + c

3x - a - b  =  c

4)

Solve 2(x + y) = z for y

First isolate x + y by getting rid of 2. To get rid of 2, divide both sides by 2.

2 / 2 (x  + y)   = z / 2

1(x + y)   = z / 2

x + y = z / 2

Subtract x from both sides of the equations

x - x + y  = (z / 2) - x

0  + y   = (z / 2) - x

y = (z / 2) - x

How to solve literal equations quiz

Recent Articles

  1. Time-series Data - Definition and Example

    May 07, 21 02:29 PM

    A time-series data shows information about the same subject or element of a sample or population for different periods of time.

    Read More