Math 7 (Period 4)

Solving Two Step Equations 4.1

Solving equations may involve using more than one inverse operation to isolate the variable (putting the variable alone on one side of the equation)

Since we are undoing the equation, we literally do PEMDAS in reverse!

3x + 8 = 23

   

 we used the  subtraction property of equality ( -  prop=)

3x + 0 = 15    

Here we have the Additive Inverse or Inverse Property of Addition  (Inv +)

We don’t want to write with “+ 0”

The Identity Property of Addition (ID+) allows us to write

3x = 15

Now we need to divide both sides by 3 and the Division Property of Equality ( ÷ prop =)  allows us to do that

3x/3 = 15/3   Multiplicative Inverse or the Inverse Property of Mult (Inv×)

1x = 5  we don’t want to write 1x ->Using the Identity Property of Multiplication (ID×)

x = 5 

and we BOX our answer.

Solving

x/4 – 12 = 1

Involves a similar process:

We need to add 12 to both sides

  we used the Addition Property of Equality ( +prop=)

x/4 + 0 = 13  

Here we have the Additive Inverse or Inverse Property of Addition  (Inv +)

We don’t want to write with “+ 0”

The Identity property of Addition (ID+) allows us to write

x/4 = 13

Now we need to multiply BOTH sides by 4/1 and the Multiplication Property of Equality (×prop=) allows us to do that.

Notice where the 4/1 is located and how it has  HUGS ( ) surrounding it! That’s required in my class! It shows that you are understanding the process of multiplying by the reciprocal of ¼.

  

Multiplicative Inverse or the Inverse Property of Mult (Inv×)

1x = 52  we don’t want to write 1x ->Using the Identity Property of Multiplication (ID×)

x = 52 

and we BOX our answer.