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Logic and Proof

Logic and Proof

Algebraic Proofs Exercises

Example 1

If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.

StatementsReasons
1. 4x + 12 = 0?

Example 2

If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.

StatementsReasons
1. 4x + 12 = 0Given
2. 4x = ­-12?

Example 3

If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.

StatementsReasons
1. 4x + 12 = 0Given
2. 4x = ­-12Subtract 12 from (1)
3. x = -3?

Example 4

If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.

StatementsReasons
1. 4x + 12 = 0Given
2. 4x = ­-12Subtract 12 from (1)
3. x = -3Divide (2) by 4
4. x2 = 9?

Example 5

If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.

StatementsReasons
1. 4x + 12 = 0Given
2. 4x = ­-12Subtract 12 from (1)
3. x = -3Divide (2) by 4
4. x2 = 9Square (3)
5. x2 + 2 = 11?

Example 6

Give the statements and the reasons that prove that if 5 – x2 = 1 and , then y = 28.

StatementsReasons
1. 5 – x2 = 1Given
2. Given
3. ??

Example 7

Give the statements and the reasons that prove that if 5 – x2 = 1 and , then y = 28.

StatementsReasons
1. 5 – x2 = 1Given
2. Given
3. -x2 = -4Subtract 5 from both sides of (1)
4. ??

Example 8

Give the statements and the reasons that prove that if 5 – x2 = 1 and , then y = 28.

StatementsReasons
1. 5 – x2 = 1Given
2. Given
3. -x2 = -4Subtract 5 from both sides of (1)
4. x2 = 4Multiply (3) by -1
5. ??

Example 9

Give the statements and the reasons that prove that if 5 – x2 = 1 and , then y = 28.

StatementsReasons
1. 5 – x2 = 1Given
2. Given
3. -x2 = -4Subtract 5 from both sides of (1)
4. x2 = 4Multiply (3) by -1
5. Substitute (4) into (2)
6. ??
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