Example 1
If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.
| Statements | Reasons |
| 1. 4x + 12 = 0 | ? |
Example 2
If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.
| Statements | Reasons |
| 1. 4x + 12 = 0 | Given |
| 2. 4x = -12 | ? |
Example 3
If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.
| Statements | Reasons |
| 1. 4x + 12 = 0 | Given |
| 2. 4x = -12 | Subtract 12 from (1) |
| 3. x = -3 | ? |
Example 4
If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.
| Statements | Reasons |
| 1. 4x + 12 = 0 | Given |
| 2. 4x = -12 | Subtract 12 from (1) |
| 3. x = -3 | Divide (2) by 4 |
| 4. x2 = 9 | ? |
Example 5
If 4x + 12 = 0, then prove that x2 + 2 = 11 using an algebraic proof.
| Statements | Reasons |
| 1. 4x + 12 = 0 | Given |
| 2. 4x = -12 | Subtract 12 from (1) |
| 3. x = -3 | Divide (2) by 4 |
| 4. x2 = 9 | Square (3) |
| 5. x2 + 2 = 11 | ? |
Example 6
Give the statements and the reasons that prove that if 5 – x2 = 1 and 
, then y = 28.
| Statements | Reasons |
| 1. 5 – x2 = 1 | Given |
| 2. | Given |
| 3. ? | ? |
Example 7
Give the statements and the reasons that prove that if 5 – x2 = 1 and , then y = 28.
| Statements | Reasons |
| 1. 5 – x2 = 1 | Given |
| 2. | Given |
| 3. -x2 = -4 | Subtract 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.
| Statements | Reasons |
| 1. 5 – x2 = 1 | Given |
| 2. | Given |
| 3. -x2 = -4 | Subtract 5 from both sides of (1) |
| 4. x2 = 4 | Multiply (3) by -1 |
| 5. ? | ? |
Example 9
Give the statements and the reasons that prove that if 5 – x2 = 1 and , then y = 28.
| Statements | Reasons |
| 1. 5 – x2 = 1 | Given |
| 2. | Given |
| 3. -x2 = -4 | Subtract 5 from both sides of (1) |
| 4. x2 = 4 | Multiply (3) by -1 |
5.  | Substitute (4) into (2) |
| 6. ? | ? |