This document contains an algebra 1 lesson on algebraic proofs. It provides examples of algebraic proofs for equations such as 9=5+4, -5=3x+1, and 2x-30=-4x+6. Each proof is shown step-by-step including the statement and reason for each step using properties of equality, addition, subtraction, multiplication, and division. The document also defines and provides examples of algebraic properties used in proofs such as the commutative, associative, and distributive properties.

1. Algebra 1
Lesson 2.8
Algebraic Proof

2. What do you know about Algebraic Proof?
Think-Pair-Share

3. Prove it!
ConceptWhy are we able to...
-frying pan
-heat
-muscles
- law of gravity
- soap & water
- washing machine
-dryer

4. Prove that your BF is cheating on you...
(
(some proof) (more proof)
JB is cheating on Ms.
Vallejo!

5. Prove: 9=5+4
Prove...
Statement Reason
(What you did) (What allowed you to do that?)
1. 9=5+4 1. Given
2. 9=9 2. Addition

6. Prove: -5 = 3x+1
Prove...
Statement Reason
(What you did) (What allowed you to do that)
1. -5 = 3x + 1 1. Given
2. 6 = 3x 2. subtraction Prop of equality
-1 -1
/3 /3
3. 2=x 3. division Prop of equality

7. Given: 5x - 4 = 6 Prove: x=3
Prove...
Statement Reason
(What you did) (What allowed you to do that?)
1. 5x - 4 = 6
+4 +4
2. 5x = 10
/5 /5
3. x= 2
1. Given
2. Addition prop of equality
3. division Prop of Equality

8. Given: 2x - 30 = -4x + 6
Prove...
Statement Reason
(What you did) (What allowed you to do that?)
1. 2x - 30 = -4x + 6
+ 4x +4x
2. 6x - 30 = 6
+30 +30
3. 6x = 36
/6 /6
4. x = 6
1. Given
2. Addition prop of Eq.
3. Addition prop of Eq
4. Division prop of Eq

9. 10
10
1. Given
2. Distributive Prop.
3. Assoc. Prop of Add.
4. Addition
1. Given
2. Commu. Prop of Mult.
3. Addition
4. Commu. Prop of Add.

10. 1. Given
2. Comm. Prop of Mult.
3. Assoc Prop of Mult.
4. Multiplication
5. Addition
1. Comm.P of Mult
2. Mult.
3. Addition

13. Commutative Property
of Addition
A B = C
B A C