Page 194 - Math Course 2 (Book 2)

Two-Column Algebraic Proof

Let’s Begin Your Turn!

Verify Algebraic Relationships

Solve –3(a + 3) + 5(3 – a) = –50.
Verify Algebraic Relationships

A. a = 12
Example B. a = –37
C. a = –7
D. a = 7
Solve 2(5 – 3a) – 4(a + 7) = 92.
Answer
Algebraic Steps Properties
2(5 – 3a) – 4(a + 7) = 92 Original equation
10 – 6a – 4a – 28 = 92 Distributive Property
–18 – 10a = 92 Substitution Property

–18 – 10a + 18 = 92 + 18 Addition Property
–10a = 110 Substitution Property
–10a
= 110 Division Property
10 –10
a = –11 Substitution Property
Write a Two-Column Proof
Answer a = –11
Which of the following reasons would complete the
proof of the if-then statement?

10 –8n
If = –2
then n = 2.
Write a Two-Column Proof 3
Example Proof:

Statements Reasons

7d + 3 10 –8n
Write a two-column proof. If = 6 1. = –2 1. Given
then d = 3. 4 3
10 –8n
Proof: 2. 3 ( ) = 3(–2) 2. ?
3
Statements Reasons 3. 10 – 8n = –6 3. Substitution

7d + 3 4.10 – 10 – 8n = – 6 – 10 4. Subtraction Property
1. = 6 1. Given
4
7d + 3
2. 4( ) = 4(6) 2. Multiplication Property 5. –8n = –16 5. Substitution
4 –8n –16
6. = 6. Division Property
3. 7d + 3 = 24 3. Substitution –8 –8
7. n = 2 7. Substitution
4. 7d + 3 – 3 = 24 – 3 4. Subtraction Property
A. Distributive Property
5. 7d = 21 5. Substitution B. Multiplication Property
7d 21 C. Division Property
6. = 6. Division Property D. Symmetric Property
7 7
7. d = 3 7. Substitution Answer

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