3.1 Addition Property of Equality (APE)

The Addition Property of EqualityRule:

if a = b, then a + c = b + c

Another Version of the Rule:If a=b, then

a+(-c)= b+(-c)

Which is the same as:If a=b, then a - c =b - c

To solve for “x”x – 8 = 11

• Goal: get “x” alone on one side of the equation.• How: do the opposite of whatever is keeping “x”

from being all by itself.• Why: by doing the opposite operation, the # on

the side of the variable cancels out to 0.• Rule: whatever you add/subtract to one side of the

equation you must add/subtract to the other.

x – 8 + 8 = 11 + 8 x =

19

Example 1: a - 5 = -2 +5 +5

a = 3

Example :2 19 = k + 7 -7 -7

12 = k

Example 3: a + 1.5 = 3.2 -1.5 -1.5

a = 1.7

Example 4:

x + 6.8 =5.2

-6.8 -6.8

__________________

X= -1.6

2

3

2

1x

11 3

2 2

1

2 2x

2

1

2

3

x

2

4 2

Example 5:

2 2

9 3m

2 2

9

2 6

9 9 9m

4

9m

Example 6:

3 1

8 4x

3 3

8

3 2

8 8 8x

5

8x

Example 7:

Example 8: A number is increased by 36 is 15. Find the number.

Let x = the original number.

x + 36 = 15

- 36 - 36x = -21

Example 9: A number decreased by 83 is 46. Find the number.

Let x = the original number.

x - 83 = 46

+83

+83

x = 129

Homework: Page 116 (2-40) even

How to set up Homework:1.Name, period, #, Page#, Problems Assigned2.Write all questions, signify the answer3. Show all work by adding/subtracting the same amount to both sides of the equal sign4. Correct it the next day in class with red pen