State the property or properties that justify the following. 5(x-2)=(x-2)(5)

The equation \( 5(x - 2) = (x - 2)(5) \) is justified by the **Commutative Property of Multiplication**.

### Explanation:
The Commutative Property of Multiplication states that the order in which two numbers (or expressions) are multiplied does not change the product. In other words, for any two numbers \(a\) and \(b\):

\[
a \times b = b \times a
\]

In the given equation:
- The left side is \( 5(x - 2) \).
- The right side is \( (x - 2)(5) \).

Since the multiplication is commutative, \( 5(x - 2) \) is equal to \( (x - 2)(5) \), which is why the equation holds true.

### Property Justification:
- **Commutative Property of Multiplication**

Would you like more details or have any questions?

Here are five related questions:
1. What is the Distributive Property of multiplication over addition?
2. How does the Associative Property of multiplication differ from the Commutative Property?
3. Can the Commutative Property be applied to subtraction? Why or why not?
4. What is an example of the Commutative Property with three factors?
5. How do you use the Distributive Property to expand an expression like \( a(b + c) \)?

**Tip:** The Commutative Property applies to both addition and multiplication but not to subtraction or division!

Explore how the Commutative Property of Multiplication applies in equations with a detailed explanation of the equation 5(x - 2) = (x - 2)(5). This problem illustrates key algebraic concepts and theorems, including the Commutative Property of Multiplication. Suitable for students in Grades 7-9.

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