Identify the property that justifies each step asked about in the answer area below.
Line 1: =
(2x+9)+5x
Line 2: , left parenthesis, 9, plus, 2, x, right parenthesis, plus, 5, x
Line 2: =
(9+2x)+5x
Line 3: , 9, plus, left parenthesis, 2, x, plus, 5, x, right parenthesis
Line 3: =
9+(2x+5x)
Line 4: , 9, plus, 7, x
Line 4: =
9+7x

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 break down the transformations step by step and identify the appropriate properties:

1. **Line 1 to Line 2:**
   \((2x + 9) + 5x \to (9 + 2x) + 5x\)

   Here, the terms inside the parentheses \((2x + 9)\) are being rearranged as \((9 + 2x)\). This is an example of **reordering the terms** within an addition, which is the **Commutative Property of Addition**.

   **Answer:** Commutative Property of Addition

2. **Line 2 to Line 3:**
   \((9 + 2x) + 5x \to 9 + (2x + 5x)\)

   In this step, the grouping of terms has changed. Initially, \(9\) was grouped with \(2x\), but now \(2x\) is grouped with \(5x\). This change in grouping reflects the **Associative Property of Addition**.

   **Answer:** Associative Property of Addition

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Would you like any further clarification on these properties?

Here are some follow-up questions that could expand your understanding:

1. What is the difference between the commutative and associative properties?
2. How would you apply the commutative property to a multiplication problem?
3. Can the associative property be applied to subtraction or division?
4. Why is it important to recognize these properties in solving algebraic expressions?
5. How does the distributive property differ from the commutative property?

**Tip:** Understanding properties like the commutative and associative properties can help simplify complex algebraic expressions efficiently!

Identify the property that justifies each step asked about in the answer area below.
Line 1: = (2x + 9) + 5x
Line 2: = (9 + 2x) + 5x
Line 3: = 9 + (2x + 5x)
Line 4: = 9 + 7x

Learn how to identify and apply the Commutative and Associative Properties of Addition in algebraic expressions. This step-by-step explanation breaks down each transformation, making it suitable for students in Grades 6-8.

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