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.

The first literal equation we will solve is ax = b. Study this first one below carefully!

Then we will show how to solve y  = mx + b which 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. 

How to solve literal equations

 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. Find the Multiplicity of a Zero

    Oct 20, 21 04:45 AM

    Learn how to find the multiplicity of a zero with this easy to follow lesson

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.