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

Line 1: , left parenthesis, 10, x, plus, 3, right parenthesis, plus, 4, x

Line 1: =

(10*x*+3)+4*x*

Line 2: , left parenthesis, 3, plus, 10, x, right parenthesis, plus, 4, x

Line 2: =

(3+10*x*)+4*x*

Line 3: , 3, plus, left parenthesis, 10, x, plus, 4, x, right parenthesis

Line 3: =

3+(10*x*+4*x*)

Line 4: , 3, plus, 14, x

Line 4: =

3+14*x*

Let's identify the property that justifies each step:

**Line 1 to Line 2:**

- **Original Expression:** \((10x + 3) + 4x\)
- **Changed to:** \((3 + 10x) + 4x\)

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

- The commutative property of addition allows us to change the order of terms being added. Here, \(10x\) and \(3\) were swapped in order.

**Line 2 to Line 3:**

- **Original Expression:** \((3 + 10x) + 4x\)
- **Changed to:** \(3 + (10x + 4x)\)

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

- The associative property of addition allows us to regroup terms without changing their order. Here, the grouping was changed to combine \(10x\) and \(4x\) together.

**Line 3 to Line 4:**

- **Original Expression:** \(3 + (10x + 4x)\)
- **Changed to:** \(3 + 14x\)

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

- This step simplifies the expression by adding the like terms \(10x\) and \(4x\) to get \(14x\).

Would you like any further explanations or have any questions? Here are some related questions:

1. Can the commutative property be applied to multiplication as well?
2. What is the difference between commutative and associative properties in terms of their application?
3. How can you identify like terms in an algebraic expression?
4. Why is it important to combine like terms when simplifying expressions?
5. How does the distributive property differ from the associative and commutative properties?

**Tip:** Practice identifying properties in various algebraic expressions to solidify your understanding and improve your problem-solving skills.

Understand how to identify properties like the commutative and associative properties of addition in algebraic expressions. This problem involves step-by-step analysis of expressions involving variables. Suitable for students in Grades 7-9.

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