Identify the property that justifies each step asked about in the answer area below.
Line 1: , left bracket, 2, x, plus, 5, right bracket, plus, x
Line 1: =
(2x+5)+x
Line 2: , left bracket, 5, plus, 2, x, right bracket, plus, x
Line 2: =
(5+2x)+x
Line 3: , 5, plus, left bracket, 2, x, plus, x, right bracket
Line 3: =
5+(2x+x)
Line 4: , 5, plus, 3, x
Line 4: =
5+3x
Line 1: Associative property of addition
Line 2: Commutative property of addition
Line 3: Associative property of addition
Line 4: Simplification
Line 1: Distributive Property
Line 2: Commutative Property
Line 3: Associative Property
Line 4: Simplification
The properties that justify each step are as follows:
1. Line 1 to Line 2: The Commutative Property of Addition is used here because we are rearranging the terms inside the parentheses. This property states that the order of addition does not affect the sum, so we can switch the order of 2x and 5.
2. Line 2 to Line 3: The Associative Property of Addition is used in this step. This property allows us to regroup the terms inside the parentheses without changing the sum. We are grouping 5 and 2x together first and then adding x separately.
3. Line 3 to Line 4: The Distributive Property is applied here. This property states that when we multiply a number (in this case, 1) by a sum or difference, we can distribute the multiplication to each term inside the parentheses. We are multiplying 1 by (2x + x), which gives us 2x + x.