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