Identify the property that justifies each step asked about in the answer area below.

Question

Line 1: 2(4+9x)
Line 2: 2(9x+4)
Line 3: 18x+8

Answer 1

To justify each step in the transformation from Line 1 to Line 3, we can use the following properties:

1. Line 1 to Line 2:

   • Property: Commutative Property of Addition
   • Justification: This property allows us to rearrange the terms inside the parentheses. The expression \( 4 + 9x \) is reordered to \( 9x + 4 \).

2. Line 2 to Line 3:

   • Property: Distributive Property
   • Justification: This property enables us to multiply each term inside the parentheses by the factor outside, thus transforming \( 2(9x + 4) \) into \( 2 \cdot 9x + 2 \cdot 4 = 18x + 8 \).

In summary:

• From Line 1 to Line 2: Commutative Property of Addition
• From Line 2 to Line 3: Distributive Property