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The problem in the image involves simplifying an algebraic expression and identifying the mathematical properties used at each step (such as associative, commutative, or distributive).

### Given Expression:
\[
5(2x + 3) + 9x
\]

### Simplification steps:

1. **Step 1:**
   Apply the **distributive property**: Multiply 5 by both terms inside the parentheses:
   \[
   5(2x + 3) + 9x = 5 \cdot 2x + 5 \cdot 3 + 9x = 10x + 15 + 9x
   \]
   The distributive property was used to expand the parentheses.

2. **Step 2:**
   Use the **commutative property** of addition to rearrange terms:
   \[
   10x + 9x + 15
   \]
   The commutative property allows rearranging terms without changing their sum.

3. **Step 3:**
   Use the **associative property** of addition to group the like terms:
   \[
   (10x + 9x) + 15 = 19x + 15
   \]
   The associative property is used to group like terms.

### Summary:
- Step 1 uses the **distributive property**.
- Step 2 uses the **commutative property**.
- Step 3 uses the **associative property**.

Would you like further details or explanations?

Here are 5 related questions you could explore:
1. What is the difference between the associative and commutative properties?
2. Can you give an example where the distributive property simplifies a more complex expression?
3. How does the order of operations affect simplifications involving these properties?
4. What happens if you apply the properties in a different order?
5. How do these properties apply to multiplication versus addition?

**Tip:** The distributive property is a powerful tool when simplifying expressions involving both addition and multiplication.

Simplify the expression 5(2x + 3) + 9x and identify the properties used.

Learn how to simplify the algebraic expression 5(2x + 3) + 9x using the distributive, commutative, and associative properties. This step-by-step guide is designed for students in Grades 6-8.

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