Transcript Chapter 3 Lesson 3 Solving Equations by Adding or Subtracting pgs

Chapter 3 Lesson 3
Solving Equations by Adding or
Subtracting
pgs. 110-114
What you will learn:
Solve equations by using the
Subtraction Property of Equality
Solve equations by using the Addition
Property of Equality
Vocabulary
Inverse operations (110): “undo” each other
Ex) x + 4 to undo the addition of 4, you would subtract 4
x+4=7
x+4-4=7-4
x+0=3
x=3
Remember:
What ever you do to one
side of the equation, you
have to do to the other side
Equivalent equations (111): two equations that equal the same
Concept check: Which integer would you subtract from each side
of x + 7 = 20 to solve the equation?
7
Concept check: Are x + 4 = 15 and x = 4 equivalent equations?
No, the solution of x + 4 = 15 is 11, not 4
Key Concept:
Subtraction Property of Equality (110):
Words:
If you subtract the same number from each side of
an equation, the two sides remain equal.
Symbols:
For any numbers a, b, and c, if a = b, then a-c = b-c
Examples:
5=5
5-3=5-3
2=2
x+2=3
x+2-2=3-2
x=1
You try!
Check:
Substitute 9 for m
m + 6 = 15
m + 6 - 6 = 15 - 6 9 + 6 = 15
15 = 15 
m=9
x + 5 = -3
x + 5 - 5 = -3 - 5
x = -8
Check: -8 + 5 = -3
-3 = -3
Graph the Solutions of an Equation:
Graph the solution of
16 + x = 14
Step 1: Solve for x
x + 16 = 14
Commutative Property of Addition
x + 16 - 16 = 14 -16 Subtract 16 from both sides
x = -2
Simplify
The solution is -2. To graph the solution, draw a dot at
-2 on a number line.

-3 -2 -1 0 1 2 3
Key Concept:
Addition Property of Equality:
Words: If you add the same number to each side of an
equation, the two sides remain equal.
Symbols: For any numbers a, b, and c,
if a = b, then a+c = b+c
Examples: 6 = 6
6+3= 6 + 3
9=9
You try!
Check:
r - 5 = 10
Sub 15 for r
r - 5 + 5 = 10 + 5 15 - 5 = 10
r = 15
10 = 10
x2 = 5
x-2+2=5+2
x=7
84 = s - 34
84 + 34 = s - 34 + 34
118 = s
Check: 84 = 118-34
84 = 84
Use an Equation to Solve a Problem:
In the 2000 presidential election, Indiana had 12 electoral votes.
That was 20 votes fewer than the number of electoral votes in
Texas. Write and solve an equation to find the number of
electoral votes in Texas.
12

Indiana’s votes
=
x - 20

20 fewer than Texas’ votes
12 = x - 20
12 + 20 = x - 20 + 20
32 = x
Texas has 32 electoral votes.
Practice:
y + 49 = 26
y + 49 - 49 = 26 - 49
y = -23
q - 8 = 16
q - 8 + 8 = 16 + 8
q = 24
-13 + k = -2
-13 + 13 + k = -2 + 13
k = 11
u - 11 = -14
u - 11 + 11 = -14 + 11
u = -3
Check:
-23 + 49 = 26
26 = 26
24 - 8 = 16
16 = 16
-13 + 11 = -2
-2 = -2
-3 - 11 = -14
-14 = -14
Take a practice sheet by the door!
Look at the problems in the book!
Use the book’s internet site!
Extra practice on pg. 729!