Literal Equations

Let’s begin by thinking about numerical equations…

• Here are two numerical equations that uses the same values. 15 = 12 + 3 12 = 15 – 3

• Notice one shows what 15 equals “in terms of” 12 and 3.• The other one shows what 12 equals “in terms of” 15 and 3.

• Could you write an equation that shows what 3 equals “in terms of” 15 and 12?

• Notice: you used “inverse operations” to rewrite the equations & maintain equality.

Now, let’s think about equations with one variable…• Here are two one variable equations that uses the same values.

12 = 5x + 2 x = (12 – 2) 5

• Notice one shows what 12 equals “in terms of” 5, 2, and x.• The other one shows what x equals “in terms of” 12, 2, and 5.

• Could you write an equation that shows what 2 equals “in terms of” 12, 5, and x?

• Notice: you are still using “inverse operations” to rewrite the equations & still maintain equality.

So - What are literal equations?

• BASICALLY – LITERAL EQUATIONS ARE LIKE ANY OTHER EQUATION THAT SHOWS HOW QUANTITIES ARE EQUAL.

• WHAT MAKES LITERAL EQUATIONS SPECIAL IS THAT THEY USE MULTIPLE VARIABLES INSTEAD OF JUST ONE!

• WE WILL STILL REARRANGE THE EQUATIONS USING INVERSE OPERATIONS.

How to read the instructions for literal equations…• Sometimes the problem will state:“Write the equation in terms of ___”

Sometimes the problem will state:“Solve _______ for _____”

Sometimes the problem will state:

“Solve for the designated variable”

No matter how it is presented…

Our goal is to get the indicated variable

alone

on the left side of the equal sign.

Let’s try it…

Example 1:

Solve for “b”: a + b = 12

STEPS:

1. Highlight the term with the designated variable.

2. Use inverse operations.

CHECK IT by substituting valuesOriginal equation

a + b = 12

Let’s choose a = 3.

That would mean b = 9.

Re-arranged equation

b = 12 - a

Replace those same values a = 3 and b = 9 into this “new” equation.

9 = 12 – 39 = 9*If we had not solved this correctly, these numbers would not work!

Let’s try it…

Example 2

Solve for “p”: m = 3n + 2p

STEPS:

1. Highlight the term with the designated variable.

2. Use inverse operations.

CHECK IT by substituting valuesOriginal equation

m = 3n + 2p

Let’s choose n = 7 and p = 5.

That would mean m = 3(7) + 2(5)or m = 31

Re-arranged equation

p =

Replace those same values n = 7 and p = 5 into this “new” equation.

5 =

*If we had not solved this correctly, these numbers would not work!

Let’s try it…

Example 3

Write equation in terms of “w”:

V = lwh

STEPS:

1. Highlight the term with the designated variable.

2. Use inverse operations.

CHECK IT by substituting valuesOriginal equation

V = lwh

Re-arranged equation

w =

Let’s try it…

Example 4

Write equation in terms of “w”:

P = 2(l+w)

STEPS:

1. Highlight the term with the designated variable.

2. Use inverse operations.

CHECK IT by substituting valuesOriginal equation

P = 2(l + w)

Re-arranged equation

w = - l

Now let’s try some together…

• Worksheet from Illustrative Mathematics.

Application

• Rectangle task from Cpalms