Question

Identify the property that justifies each step about the answer and the area below. Line 1: (6+x)x line 2: x(x6+x) line 3: x(x+6). line one to line is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property. Line 2 to line 3 is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property

Answer 1

Let's break down each transition in the steps you've provided and identify the appropriate properties that justify each step.

1. **From Line 1: (6 + x)x to Line 2: x(6 + x)**
- This change involves switching the order of multiplication, which is justified by the **Commutative Property of Multiplication**. It states that changing the order of factors does not change the product.

2. **From Line 2: x(6 + x) to Line 3: x(x + 6)**
- This step involves reordering the terms within the parentheses, which can be justified by the **Commutative Property of Addition**. This property states that changing the order of terms in an addition does not change the sum.

In summary:
- The property that justifies the transition from Line 1 to Line 2 is the **Commutative Property of Multiplication**.
- The property that justifies the transition from Line 2 to Line 3 is the **Commutative Property of Addition**.

So, the complete identifications are:
- **Line 1 to Line 2**: Commutative Property of Multiplication
- **Line 2 to Line 3**: Commutative Property of Addition