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

Line 1: , 9, left parenthesis, 8, plus, 7, x, right parenthesis
Line 1: =
9(8+7x)
Line 2: , 9, left parenthesis, 7, x, plus, 8, right parenthesis
Line 2: =
9(7x+8)
Line 3: , 63, x, plus, 72
Line 3: =
63x+72

1 answer

Here are the properties that justify each step in your expression:

Line 1: From \( 9(8 + 7x) \) to \( 9(7x + 8) \)
Property: Commutative Property of Addition
Justification: The Commutative Property of Addition states that the order of addition does not affect the sum. Therefore, \( 8 + 7x \) can be rearranged to \( 7x + 8 \).

Line 2: From \( 9(7x + 8) \) to \( 63x + 72 \)
Property: Distributive Property
Justification: The Distributive Property allows us to multiply each term inside the parentheses by the factor outside. Thus, multiplying \( 9 \) by \( 7x \) yields \( 63x \) and multiplying \( 9 \) by \( 8 \) yields \( 72 \).

In summary:

  1. Commutative Property of Addition for Line 1.
  2. Distributive Property for Line 2.