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# Algebraic Proofs Exercises

### 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. ? ?