3.1 Addition Property of Equality
(APE)
• Goals: To use the APE to solve equations
and word problems
The Addition Property of Equality
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.
• Do the opposite of whatever is
keeping “x” from being all by itself.
x – 8 + 8 = 11 + 8
x = 19
Show your work exactly like this:
Write the problem:
x+7=2
Add same number to
-7 -7
both sides of “=“:
Write answer with
box around it
x = -5
y - 8 = -3
+8 +8
y =5
a - 5 = -2
+5 +5
a=3
19 = k + 7
-7
-7
12 = k
a + 1.5 = 3
-1.5 -1.5
a = 1.5
1
3
x 
2
2
1 1
3 1
x    
2 2
2 2
 3 1
x

2
2
4


2
2
3
1
x 
4
4
3 3
1 3
x    
4 4
4 4
1  3

4
1

2
2
m 
9
2 2
m  
9 9
2
3
6 2

9 9
4
m
9
3 1
x 
8 4
3 3 2 3
x   
8 8 8 8
5
x
8
A number is increased by 36 is 15.
Find the number.
Let x = the original number.
x + 36 = 15
- 36 - 36
x = -21
A number decreased by 83 is 46.
Find the number.
Let x = the original number.
x - 83 = 46
+83
+83
x = 129
The weekly rent on an apartment was
increased by $82. The new rental cost is
$675. What is the previous rent?
Let x = the previous rent.
x + 82 = 675
- 82 - 82
x = 593
Assignment
Page 116
(2-40) even
Must write problem and show
adding same amount to both sides
of equal, then the solution.