Problem 5.1: Name the property shown:
x = 12 and 12 = y. Thus, x = y [Solution]

Problem 5.2: Name the property shown:
4(2x) = 8x [Solution]

Problem 5.3: What number, when multiplied by 3, is equal to 1? [Solution]

Problem 5.4: What number, when multiplied by

, is equal to 1? [Solution]

Problem 5.5: Name the property or operation used in each step:
Solve for x:

- 16 = - 4

1. 
   - 16 = - 4
2. 
   - 16 + 16 = - 4 + 16
3. 
   + 0 = 12
4. 
   = 12
5. 12(
   
   ) = 12(12)
6. 1x = 144
7. x = 144

[Solution]

Problem 5.6: Name the property or operation used in each step:
Solve for y: 3(4y + 3) = 9

1. 3(4y + 3) = 9
2. 12y + 9 = 9
3. 12y + 9 - 9 = 9 - 9
4. 12y + 0 = 0
5. 12y = 0
6. 12 = 0ory = 0
7. Since 12≠ 0, y = 0

[Solution]

Problem 5.7: Name the property or operation used in each step:
Solve for x if y = 4: 4y + 5 = 3(x + 1)

1. 4y + 5 = 3(x + 1)
2. 4(4) + 5 = 3(x + 1)
3. 16 + 5 = 3(x + 1)
4. 21 = 3(x + 1)
5. 
   =
   
6. 7 = 1(x + 1)
7. 7 = x + 1
8. 7 - 1 = x + 1 - 1
9. 6 = x + 0
10. 6 = x
11. x = 6

[Solution]