Logic and Proof True or False

1. What property of equality would you use to solve for x in the equation 5x = 15? -> Symmetry
2. Which is an example of the symmetric property of equality? -> If A = B and B = C, then A = C
3. Which of these is not a property of equality (and therefore congruence)? -> Transitivity
4. Which property lets us simplify the equation (10 – 5)2x – (10 – 5) = 0 to 52x – 5 = 0? -> Reflexive Property
5. We are given that A = B and C = D. What would make the statement A/C = B/D untrue? -> D = 0
6. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. y⁄x – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 3? -> 2x = -6
7. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. y⁄x – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 4? -> x = 3
8. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. y⁄x – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 5? ->

9. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. y⁄x – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 6? ->

10. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.

StatementsReasons
1. 2x + 7 = 1Given
2. y⁄x – 1 = 2Given
3. ?Subtract 7 from both sides of (1)
4. ?Divide (3) by 2
5. ?Substitute (4) into (2)
6. ?Add 1 to both sides of (5)
7. ?Multiply (6) by –3

Which of the following fits best for statement 7? -> x = -9

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