1. 2.5 – Reasoning Using Properties of Algebra

2. If a = b, then a + c = b + c If a = b, then a – c = b – c
Name
Property of Equality
Addition Property
Subtraction Property
Multiplication Property
Division Property
If a = b, then a + c = b + c
If a = b, then a – c = b – c
If a = b, then ac = bc
If a = b, then a/c = b/c
Distribution Property
If a(x + b), then ax + ab
Substitution Property
If a = b, then b can be substituted in for a

3. a = a If a = b, then b = a If a = b and b = c, then a = c
Reflexive Property
Symmetric Property
Transitive Property
a = a
If a = b, then b = a
If a = b and b = c, then a = c
Reflexive Repeats
Symmetric Switches

4. 1. Use the property to complete the statement.
a. Multiplication Property of Equality:
If m1 = m2, then 3m1 = ____________.
b. Substitution Property of Equality:
If a = 20, then 5a = __________.
3m2
5(20) = 100

5. Statement Reason If 4(x + 7), then 4x + 28 If 2x + 5 = 9, then 2x = 4
Distributive Prop
9 + 2 = 9 + 2
Reflexive Prop
Subtraction Prop
If 4x + 7 = 11, then 4x = 4. If 4x = 4, then x = 1.
Transitive Prop
Addition Prop
4 + 5 = 5 + 4
Symmetric Prop
Division Prop

6. 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.

7. Format of Proofs
Given:
Picture
Prove:
Statements Reasons 1. 2. 3. …
What you are given 1. 2. 3. …
Given
To Prove

8. given Addition Prop Division Prop Statements Reasons 1. 8x – 34 = 6
Complete the logical argument by writing a reason for each step.
Statements
Reasons
x – 34 = 6
1. __________________
x = 40
2. __________________
x = 5
3. __________________
given
Addition Prop
Division Prop

9. given Subtraction Prop Addition Prop Division Prop Statements Reasons
Complete the logical argument by writing a reason for each step.
Statements
Reasons
x – 7 = 6x + 7
1. __________________
x – 7 = 7
2. __________________
x = 14
3. __________________
x = -7
4. __________________
given
Subtraction Prop
Addition Prop
Division Prop

10. given Distributive Prop Combine Like Terms Addition Prop Addition Prop
Complete the logical argument by writing a reason for each step.
Statements
Reasons
(x – 3) + 1 = 4(x + 2)
1. _______________________
x – = 4x + 8
2. _______________________
x – 14 = 4x + 8
3. _______________________
x – 14 = 8
4. _______________________
x = 22
5. _______________________
given
Distributive Prop
Combine Like Terms
Addition Prop
Addition Prop

11. 1. 1. Given 2. 2. Subtraction Prop. 3. 3. Addition Prop. 4. x = 10 4.
4. Solve the equation. Write a reason for each step
4x – 9 = 2x + 11
Statements
Reasons 1.
4x – 9 = 2x + 11 1.
Given 2.
2x – 9 = 11 2.
Subtraction Prop. 3.
2x = 20 3.
Addition Prop. 4.
x = 10 4.
Division Prop.

12. 1. 12x – 3y = 30 1. Given 2. –3y = -12x + 30 2. Subtraction Prop. 3.
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.

13. HW Problem # 17 1. 12 – 3y = 30x 1. Given 2. –3y = 30x – 12 2.
Section
Page #
Assignment
Spiral ?s
2.5
3-5, 7, 9, 17, 21-26, 41, 42
12-17
# 17
Statements
Reasons 1.
12 – 3y = 30x 1.
Given 2.
–3y = 30x – 12 2.
Subtraction Prop. 3.
y = –10x + 4 3.
Division Prop.