Transcript 2.5 PowerPoint

2.5 – Reasoning Using Properties of Algebra
Name
Addition Property
Property of Equality
If a = b, then a + c = b + c
Subtraction Property
If a = b, then a – c = b – c
Multiplication
Property
Division Property
If a = b, then ac = bc
Distribution
Property
Substitution
Property
If a = b, then a/c = b/c
If a(x + b), then ax + ab
If a = b, then b can be substituted in for a
Reflexive Property
a=a
Symmetric Property
If a = b, then b = a
Transitive Property
If a = b and b = c, then a = c
Reflexive Repeats
Symmetric Switches
1. Use the property to complete the statement.
a. Multiplication Property of Equality:
3m2
If m1 = m2, then 3m1 = ____________.
b. Substitution Property of Equality:
5(20) = 100
If a = 20, then 5a = __________.
Statement
If 4(x + 7), then 4x + 28
9+2=9+2
If 2x + 5 = 9, then 2x = 4
Reason
Distributive Prop
Reflexive Prop
Subtraction Prop
If 4x + 7 = 11, then 4x = 4. If 4x = 4, then
x = 1.
Transitive Prop
If x – 7 = 2, then x = 9
Addition Prop
4+5=5+4
If 4x = 12, then x = 3
Symmetric Prop
Division Prop
PROOFS!
All proofs start and end the same. It is very
helpful to have a picture to refer to. We are
given information and then are told to prove
something.
Format of Proofs
Given:
Prove:
Picture
Statements
Reasons
1. What you are given 1. Given
2.
2.
3.
3.
… To Prove
…
Complete the logical argument by writing a reason for each step.
Statements
1.
8x – 34 = 6
Reasons
1.
given
__________________
2.
8x = 40
2.
Addition Prop
__________________
3.
x=5
3.
Division Prop
__________________
Complete the logical argument by writing a reason for each step.
Statements
Reasons
1.
4x – 7 = 6x + 7
1.
given
__________________
2.
-2x – 7 = 7
2.
__________________
Subtraction Prop
3.
-2x = 14
3.
Addition Prop
__________________
4.
x = -7
4.
Division Prop
__________________
Complete the logical argument by writing a reason for each step.
Statements
Reasons
1.
5(x – 3) + 1 = 4(x + 2)
1.
given
_______________________
2.
5x – 15 + 1 = 4x + 8
2.
Distributive Prop
_______________________
3.
5x – 14 = 4x + 8
4.
5.
x – 14 = 8
x = 22
Combine Like Terms
3. _______________________
4.
Addition Prop
_______________________
5.
Addition Prop
_______________________
4. Solve the equation. Write a reason for each step
4x – 9 = 2x + 11
Statements
1.
4x – 9 = 2x + 11
Reasons
1.
Given
2. 2x – 9 = 11
2.
Subtraction Prop.
3.
2x = 20
3.
Addition Prop.
4.
x = 10
4.
Division Prop.
5. Solve the equation for y. Write a reason for each step.
12x – 3y = 30
Statements
Reasons
1. 12x – 3y = 30
1. Given
2. –3y = -12x + 30
2. Subtraction Prop.
3.
y = 4x – 10
3. Division Prop.
HW Problem
Section
2.5
Page #
108-111
Assignment
Spiral ?s
3-5, 7, 9, 17, 21-26, 41, 42 12-17
# 17
Statements
1. 12 – 3y = 30x
2.
–3y = 30x – 12
3.
y = –10x + 4
Reasons
1. Given
2. Subtraction Prop.
3. Division Prop.