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.

For example, y  = mx + b is a literal equation. See below how we solve for x as we solve for x in 8 = 2x + 4 

 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




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