1. Today:
Khan Due Tonight
Warm-Up: Review
Properties of Equality
Introduction to Algebraic Proofs
Class Work

2. Warm-Up:
1. Solve for x: 6xy - z = - 8
10
2. 4•(- 2) + (4 - 6) + 23
15 - 3•6 + 23 - 3
4. 8 +
ퟐ
ퟑ
ퟏ
ퟐ
3. - x + 4 = - x +
x = 18
ퟑ
ퟐ
x
5.
ퟑ
ퟓ
+
ퟓ
ퟔ

4. a(b + c) = ab + ac
3(5 + 7) 15 + 21 = 36
Multiplying the sum of two numbers is the
same as multiplying each term by the number

5. Properties of Equality:
Write an example of the distributive property

6. Review: Properties of Equality
Write the property described:
Reflexive Property
Symmetric
Property
1. A tie score in a basketball game
2. 36 inches = 1 yard, 1 yard = 3 feet, therefore,
36 inches = 3 feet.
3.
Transitive Property

7. Warm-Up/Test Prep:
4. = .15
Name the missing property
5.
Substitution Property
Statements Reasons
1. 2(3x + 4) = 56 1. Given
2. 6x + 8 = 56 2. Distributive Property
3. 6x + 8 – 8 = 56 – 8 3. Subtraction POE

8. Warm-Up/Test Prep:
Name the missing property
6.
7.
Distributive Property
Substitution Property

9. Two Column Proof
A two-column proof, or formal proof contains
statements and reasons organized in two columns.
In a two column proof each step is called a
statement and the properties that justify each step
are called reasons

10. ALGEBRAIC PROOFS
Proof: An argument that uses logic, definitions,
properties, and previously proven statements to show
that a conclusion is true.
Algebraic proofs use properties to prove
relationships. Reflexive, Symmetric, Transitive,
Addition & Subtraction, Multiplication & Division,
Substitution, and Distributive Properties
A group of algebraic steps used to solve problems
form a deductive argument.

11. Example 1:
Solve 3(x – 2) = 42
 Algebraic Steps Properties
3(x – 2) = 42 Given
3x – 6 = 42 Distributive Property
3x – 6 + 6 = 42 + 6 Addition Property
3x = 48 Substitution Property
3x/3 = 48/3 Division Property
X = 16 Substitution Property

12. Proofs; Example 2:
If 3(x – 2) = 3, then x = 3
Statements Reasons
3(x – 2) = 3 Given
3x – 6 = 3
3x – 6 + 6 = 3 + 6
3x = 9
3x/3 = 9/3
X = 3
Distributive property
Addition property
Substitution property
Division Property
Substitution property

13. Last Example:

15. 3. Solve for z: 6xy - z = - 8
8. If
ퟐ
ퟓ
x =
풙
ퟒퟓ
10
, then x = ?