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In the provided image, the problems from 17 to 32 ask you to identify and express one of the basic properties of real numbers (likely from a list of properties such as commutative, associative, distributive, identity, or inverse) to justify each expression. Below, I'll go through some of the problems and explain the corresponding property:

### Problem Analysis:

17. \( (2 + 3) + 5 = 2 + (3 + 5) \)
   - **Property**: Associative property of addition. It shows that the way numbers are grouped does not affect the sum.

18. \( [(1)(2)](3In the provided image, the problems from 17 to 32 ask you to identify and express one of the basic properties of real numbers (likely from a list of properties such as commutative, associative, distributive, identity, or inverse) to justify each expression. Below, I'll go through some of the problems and explain the corresponding property:

### Problem Analysis:

17. \( (2 + 3) + 5 = 2 + (3 + 5) \)
   - **Property**: Associative property of addition. It shows that the way numbers are grouped does not affect the sum.

18. \(   = [(2)(1)](3In the provided image, the problems from 17 to 32 ask you to identify and express one of the basic properties of real numbers (likely from a list of properties such as commutative, associative, distributive, identity, or inverse) to justify each expression. Below, I'll go through some of the problems and explain the corresponding property:

### Problem Analysis:

17. \( (2 + 3) + 5 = 2 + (3 + 5) \)
   - **Property**: Associative property of addition. It shows that the way numbers are grouped does not affect the sum.

18. \(   =   \)
   - **Property**: Commutative property of multiplication. It shows that the order of multiplication does not affect the product.

19. \( (x + y) + 3 = (y + x) + 3 \)
   - **Property**: Commutative property of addition. It demonstrates that the sum is the same regardless of the order of the terms.

20. \( (a + 2) + \pi = \pi + (a + 2) \)
   - **Property**: Commutative property of addition. It shows that the sum remains the same regardless of the order.

21. \( [(2)(\frac{1}{2})]z = 2[(\frac{1}{2})(z)] \)
   - **Property**: Associative property of multiplication. This reflects that the grouping of numbers in multiplication does not affect the product.

22. \( (1 + 2)(-3) = 1(-3) + 2(-3) \)
   - **Property**: Distributive property. It shows how multiplication distributes over addition.

### Detailed Explanation for Selected Problems:

- **Associative Property**: This property states that how numbers are grouped in addition or multiplication does not affect the result. For example, in Problem 17, the grouping of terms is changed without affecting the sum.

- **Commutative Property**: This property states that the order in which two numbers are added or multiplied does not change the result. For example, Problem 19 shows that \( x + y \) and \( y + x \) yield the same result.

- **Distributive Property**: This property connects addition and multiplication. It states that \( a(b + c) = ab + ac \), as seen in Problem 22.

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Would you like a detailed breakdown of more problems or any specific property? 

Here are five related questions you could consider:

1. What is the difference between the commutative and associative properties?
2. How is the distributive property used in algebraic expansions?
3. Can the inverse property be applied to subtraction or division, and how?
4. Why does the identity property for addition always involve the number zero?
5. How does the commutative property affect solving linear equations?

**Tip**: Remember that the commutative property only works for addition and multiplication, not for subtraction or division.

En los problemas 17 a 32, exprese una de las propiedades básicas del sistema de los números reales para justificar cada una de las expresiones dadas.

Explore how to solve mathematical problems using the basic properties of real numbers, including commutative, associative, distributive, identity, and inverse properties. Each problem from 17 to 32 demonstrates how these properties apply to justify the expressions.

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