Answer :
To solve this problem, let's analyze the properties of equality to determine the most appropriate one for the statement.
The problem states:
"The ______ Property of Equality states that for any numbers [tex]\( a \)[/tex] and [tex]\( b \)[/tex], if [tex]\( a = b \)[/tex], then [tex]\( b = a \)[/tex]."
We need to choose the best answer from the given options, which are:
1. Transitive
2. Associative
3. Symmetric
### Analyzing Each Property:
#### Transitive Property of Equality:
The Transitive Property of Equality states that if [tex]\( a = b \)[/tex] and [tex]\( b = c \)[/tex], then [tex]\( a = c \)[/tex]. This is not what the problem is describing, as the problem does not involve a third number [tex]\( c \)[/tex].
#### Associative Property of Equality:
The Associative Property generally applies to addition or multiplication and how the grouping of numbers does not affect the result, for example, [tex]\( (a + b) + c = a + (b + c) \)[/tex]. This property is not relevant to equality statements directly in the form given in this problem.
#### Symmetric Property of Equality:
The Symmetric Property of Equality states that if [tex]\( a = b \)[/tex], then [tex]\( b = a \)[/tex]. This exactly matches the description given in the problem. It asserts that the equality relation is reversible.
### Conclusion:
The property that the problem describes is the Symmetric Property of Equality. Hence, the best answer to this question is:
Symmetric
The problem states:
"The ______ Property of Equality states that for any numbers [tex]\( a \)[/tex] and [tex]\( b \)[/tex], if [tex]\( a = b \)[/tex], then [tex]\( b = a \)[/tex]."
We need to choose the best answer from the given options, which are:
1. Transitive
2. Associative
3. Symmetric
### Analyzing Each Property:
#### Transitive Property of Equality:
The Transitive Property of Equality states that if [tex]\( a = b \)[/tex] and [tex]\( b = c \)[/tex], then [tex]\( a = c \)[/tex]. This is not what the problem is describing, as the problem does not involve a third number [tex]\( c \)[/tex].
#### Associative Property of Equality:
The Associative Property generally applies to addition or multiplication and how the grouping of numbers does not affect the result, for example, [tex]\( (a + b) + c = a + (b + c) \)[/tex]. This property is not relevant to equality statements directly in the form given in this problem.
#### Symmetric Property of Equality:
The Symmetric Property of Equality states that if [tex]\( a = b \)[/tex], then [tex]\( b = a \)[/tex]. This exactly matches the description given in the problem. It asserts that the equality relation is reversible.
### Conclusion:
The property that the problem describes is the Symmetric Property of Equality. Hence, the best answer to this question is:
Symmetric
