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


Line 1: =
(−7x+3)+2x
Line 2: , left parenthesis, 3, plus, left parenthesis, minus, 7, x, right parenthesis, right parenthesis, plus, 2, x
Line 2: =
(3+(−7x))+2x
Line 3: , 3, plus, left parenthesis, minus, 7, x, plus, 2, x, right parenthesis
Line 3: =
3+(−7x+2x)
Line 4: , 3, plus, left parenthesis, minus, 5, x, right parenthesis
Line 4: =
3+(−5x)

Answer (pick one for each):
Line 1 to Line 2:

Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Distributive Property


Line 2 to Line 3:
Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Distributive Property




Let's go through the steps and identify the properties used.

### Line 1 to Line 2:
- **Line 1**: \((−7x+3)+2x\)
- **Line 2**: \((3+(−7x))+2x\)

The change here is a rearrangement of the terms within the parentheses. Specifically, \(3\) and \(-7x\) are swapped. This is the **Commutative Property of Addition**, which allows you to change the order of terms being added.

Answer: **Commutative Property of Addition**

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### Line 2 to Line 3:
- **Line 2**: \((3+(−7x))+2x\)
- **Line 3**: \(3+(−7x+2x)\)

In this step, the parentheses are regrouped so that the terms \(-7x\) and \(2x\) are combined inside the parentheses. This is the **Associative Property of Addition**, which allows you to change the grouping of terms in an addition problem without changing the result.

Answer: **Associative Property of Addition**

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Would you like further clarification, or do you have any additional questions? Here are some related questions:

1. What is the difference between the commutative and associative properties?
2. Can the distributive property be used in this problem? If so, where?
3. Why is the commutative property only valid for addition and multiplication, but not for subtraction?
4. How does combining like terms apply in this context?
5. How could this problem be approached using factoring?

**Tip:** The **associative property** involves grouping terms, while the **commutative property** involves changing their order.

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

Line 1: =(−7x+3)+2x
Line 2: , left parenthesis, 3, plus, left parenthesis, minus, 7, x, right parenthesis, right parenthesis, plus, 2, x
Line 2: =(3+(−7x))+2x
Line 3: , 3, plus, left parenthesis, minus, 7, x, plus, 2, x, right parenthesis
Line 3: =3+(−7x+2x)
Line 4: , 3, plus, left parenthesis, minus, 5, x, right parenthesis
Line 4: =3+(−5x)

Answer (pick one for each):
Line 1 to Line 2:

Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Distributive Property

Line 2 to Line 3:
Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Distributive Property

Learn how to identify the properties of addition used in algebraic expressions. This problem demonstrates the commutative and associative properties of addition, suitable for students in Grades 6-8.

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