Identify the property that justifies each step asked about in the answer area below.
Line 1: , left parenthesis, 7, plus, 6, x, right parenthesis, plus, 3
Line 1: =
(7+6x)+3
Line 2: , left parenthesis, 6, x, plus, 7, right parenthesis, plus, 3
Line 2: =
(6x+7)+3
Line 3: , 6, x, plus, left parenthesis, 7, plus, 3, right parenthesis
Line 3: =
6x+(7+3)
Line 4: , 6, x, plus, 10
Line 4: =
6x+10
Answer
Attempt 1 out of 2

Let's identify the property that justifies each step:

**Line 1 to Line 2:**

- **Original Expression:** \((7 + 6x) + 3\)
- **Changed to:** \((6x + 7) + 3\)

**Property Used:** **Commutative Property of Addition**

- This property states that the order in which two numbers are added does not affect the sum. Here, the terms \(7\) and \(6x\) were rearranged.

**Line 2 to Line 3:**

- **Original Expression:** \((6x + 7) + 3\)
- **Changed to:** \(6x + (7 + 3)\)

**Property Used:** **Associative Property of Addition**

- This property states that the way in which numbers are grouped when adding does not affect the sum. Here, the grouping of the terms was changed.

**Line 3 to Line 4:**

- **Original Expression:** \(6x + (7 + 3)\)
- **Changed to:** \(6x + 10\)

**Property Used:** **Simplification or Addition**

- This step simplifies the expression by performing the arithmetic operation \(7 + 3\), which results in \(10\).

Would you like any more details or have any questions? Here are some related questions:

1. What is the difference between the commutative and associative properties?
2. Can the commutative property be applied to subtraction or division?
3. How do you identify which property is used in an equation?
4. Why is simplification often the last step in solving an equation?
5. Can the associative property apply to multiplication as well?

**Tip:** Understanding these fundamental properties of numbers helps in simplifying and solving more complex algebraic expressions efficiently.

Explore how properties of addition like commutative and associative properties are applied in algebraic expressions. This problem involves simplifying expressions step-by-step, focusing on fundamental algebraic concepts. Suitable for middle school students.

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