Question

Identify the property that justifies each step asked about in the answer area below. Line 1: , left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 7, plus, 4, x, right parenthesis Line 1: = (x+6)(7+4x) Line 2: , left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 4, x, plus, 7, right parenthesis Line 2: = (x+6)(4x+7) Line 3: , left parenthesis, 4, x, plus, 7, right parenthesis, left parenthesis, x, plus, 6, right parenthesis Line 3: = (4x+7)(x+6) Answer Attempt 1 out of 2 Line 1 to Line 2: Line 2 to Line 3:

Answer 1

To identify the properties that justify each step, let's analyze the transformations made in each transition:

### Line 1 to Line 2:
- **Property:** Commutative Property of Addition
- **Justification:** The order of the terms can be rearranged in addition. The expression (7 + 4x) is rearranged to (4x + 7).

### Line 2 to Line 3:
- **Property:** Commutative Property of Multiplication
- **Justification:** The order of the factors can be swapped in multiplication. The expression (x + 6)(4x + 7) is rearranged to (4x + 7)(x + 6).

So the identified properties are:
- **Line 1 to Line 2:** Commutative Property of Addition
- **Line 2 to Line 3:** Commutative Property of Multiplication