Transcript 2_6 Algebraic Proof Day 2

Bell Ringer: Fill in the Blanks
Statements
Reasons
(4x+6)/2 = 9
Given
1. ___[(4x+6)/2] = 2(9) Multiplication Property
4x + 6 = 18
2. _________________
4x + 6 – 6 = 18 – 6
3. _________________
4. 4x = _____________ Substitution
5. (4x/4) = __________ Division Property
6. _________________ Substitution
Bell Ringer: Fill in the Blanks
Statements
Reasons
(4x+6)/2 = 9
Given
1. 2[(4x+6)/2] = 2(9)
Multiplication Property
4x + 6 = 18
2. Substitution
4x + 6 – 6 = 18 – 6
3. Subtraction Property
4. 4x = 12
Substitution
5. (4x/4) = 12/4
Division Property
6. x = 3
Substitution
Homework Solutions
14. Transitive Property
15. Substitution Property
16. Substitution Property
17. Substitution Property
18. Division or Multiplication Property
19. Reflexive Property
20.Distibributive Property
21. Substitution
22. Division or Multiplication Property
23. Transitive Property
COLLECT HOMEWORK
Objective and Homework
 Objective: Students will be able to…
* identify properties of equality for real numbers
* use properties of equality for real numbers to write two-column
proofs
 Homework
 2.6 pg 98-99 (24-27, 37, 38) Due Monday, October 31
2.6 Algebraic Proof Day 2
Thursday, October 27
Two-Column Proof
 Used to prove conjectures and theorems
 A two-column proof, or formal proof, contains
statements and reasons organized in two columns
 Each step is called a statement
 The properties that justify each step are called reasons
Make sure you have your notes
from yesterday!!
In a two-column proof
 The first statement is always the given problem
 The first reason is always Given
 The statement column goes through each step in order to
solve
 The reason column must justify each step in the statement
column using the properties for equality
Given: 4x + 8 = x + 2
Prove: x = -2
 Rearrange the statements to make a logical order in the table
A) 4x + 8 = x + 2
B) 3x + 8 = 2
C) (3x)/3 = –6/3
D) 3x = –6
F) 3x + 8 – 8 = 2 – 8
E) 4x + 8 – x = x + 2 – x
G) x = –2
Statements
Reason
1.
Given
2.
Multiplication Property
3.
Substitution
4.
Subtraction Property
5.
Substitution
6.
Division Property
7.
Substitution
Given: 4x + 8 = x + 2
Prove: x = -2
 Rearrange the statements to make a logical order in the table
Statements
Reason
1. A) 4x + 8 = x + 2
2. E) 4x + 8 – x = x + 2 – x
3. B) 3x + 8 = 2
4. F) 3x + 8 – 8 = 2 – 8
5. D) 3x = –6
6. C) (3x)/3 = –6/3
7. G) x = –2
Given
Multiplication Property
Substitution
Subtraction Property
Substitution
Division Property
Substitution
Given: 8x – 5 = 2x + 1
Statements
Prove: x = 1
Reasons
Given
6x – 5 + 5 = 1 + 5
x=1
Addition Property
Given: 8x – 5 = 2x + 1
Prove: x = 1
Statements
Reasons
8x – 5 = 2x + 1
Given
8x – 5 – 2x = 2x + 1 – 2x
Subtraction Property
6x – 5 = 1
Substitution
6x – 5 + 5 = 1 + 5
Addition Property
6x = 6
Substitution
(6x)/6 = 6
Division Property
x=1
Substitution Property
Given: 5(n – 3) = 4(2n – 7) – 14
Prove: n = 9
Make your own 2-column proof!
Homework
 2.6 pg 98-99 (24-27, 37, 38) Due Monday, October 31
 ENJOY YOUR LONG WEEKEND!!!!