https://file.aiquickdraw.com/mathbot/file/1726024365072ry63zzeo.jpg

Let's identify the mathematical properties used in the image:

1. **\(2(x + 3) = 2x + 6\)**: This is the **Distributive Property**. It shows how multiplication is distributed over addition.

2. **\(3 + (2 + 9) = (3 + 2) + 9\)**: This is the **Associative Property of Addition**. It shows that when adding three or more numbers, the grouping of the numbers does not affect the sum.

3. **\(r \cdot s = s \cdot r\)**: This is the **Commutative Property of Multiplication**. It shows that the order of multiplication does not affect the product.

Lastly, you are asked to create your own example demonstrating one of the properties above. Here's an example using the **Commutative Property of Addition**:
\[ 4 + 5 = 5 + 4 \]

Do you want more details or have any questions about the properties?

### Related questions:
1. How does the distributive property apply to subtraction?
2. What is the difference between associative and commutative properties?
3. Can the distributive property be used with multiplication over subtraction?
4. Is there an associative property of multiplication? How does it work?
5. How would the commutative property work with division?

### Tip:
Understanding these properties helps simplify algebraic expressions, making solving equations easier!

Identify the property used for the following equations:
1) 2(x + 3) = 2x + 6
2) 3 + (2 + 9) = (3 + 2) + 9
3) r • s = s • r
Create your own example demonstrating one of the properties.

Learn how to identify the Distributive, Associative, and Commutative properties with examples like 2(x + 3) = 2x + 6. This lesson covers key algebraic concepts for students in Grades 6-8.

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