Certainly! Let's take a detailed look at the given equation: [tex]\(7x = 7x\)[/tex].
1. Analyze the Equation: The equation suggests that the expression [tex]\(7x\)[/tex] is equal to itself, which means there is no change between the two sides of the equation.
2. Understand the Mathematical Properties:
- Commutative Property: This property applies to addition and multiplication, stating that the order of numbers does not change the result. For example, [tex]\(a + b = b + a\)[/tex] or [tex]\(a \times b = b \times a\)[/tex]. This property doesn't apply here because there is no ordering involved in [tex]\(7x = 7x\)[/tex].
- Reflexive Property: This property states that any mathematical expression is equal to itself. This is precisely what is being shown by [tex]\(7x = 7x\)[/tex].
- Multiplication Property of Equality: This property states that if two quantities are equal, multiplying both sides by the same number will keep the equality valid. However, this property is not needed to demonstrate the given equation.
- Transitive Property: If [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]. This property is about relating three different expressions via equality. It is not applicable here since only one expression is present.
3. Evaluate the Answer Choices:
- Commutative: Incorrect, as explained, it doesn't apply here.
- Reflexive: Correct, since [tex]\(7x = 7x\)[/tex] directly illustrates that an expression is equal to itself.
- Multiplication property of equality: Incorrect, as this property is not used in demonstrating that [tex]\(7x\)[/tex] is equal to itself.
- Transitive: Incorrect, as this involves three entities and we only have one here.
- None of the other answers are correct: Incorrect, since we identified the Reflexive property as applicable.
Based on this detailed analysis, the correct answer is:
O Reflexive
