Which Property Justifies This Statement?If $12 = X + 5$, Then $x + 5 = 12$.A. Addition Property Of Equality B. Symmetric Property Of Equality C. Reflexive Property Of Equality D. Subtraction Property Of Equality

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Introduction

In mathematics, properties of equality are essential to understand and apply when solving equations and inequalities. These properties help us manipulate expressions and equations to find the solution. In this article, we will explore the properties of equality and determine which property justifies the given statement.

Properties of Equality

There are three main properties of equality: Reflexive Property, Symmetric Property, and Transitive Property. However, when it comes to the given statement, we need to focus on the Symmetric Property of Equality.

Symmetric Property of Equality

The Symmetric Property of Equality states that if two expressions are equal, then their order can be reversed without changing the equality. In other words, if $a = b$, then $b = a$.

Example

Let's consider an example to illustrate the Symmetric Property of Equality. Suppose we have the equation $2 + 3 = 5$. Using the Symmetric Property, we can rewrite the equation as $5 = 2 + 3$.

Given Statement

The given statement is: If $12 = x + 5$, then $x + 5 = 12$. We need to determine which property of equality justifies this statement.

Analysis

Let's analyze the given statement. We have the equation $12 = x + 5$. Using the Symmetric Property of Equality, we can rewrite the equation as $x + 5 = 12$. This is because the order of the expressions can be reversed without changing the equality.

Conclusion

Based on the analysis, we can conclude that the Symmetric Property of Equality justifies the given statement. The Symmetric Property states that if two expressions are equal, then their order can be reversed without changing the equality. In this case, we have the equation $12 = x + 5$, and using the Symmetric Property, we can rewrite the equation as $x + 5 = 12$.

Answer

The correct answer is:

  • B. Symmetric Property of Equality

Other Options

Let's analyze the other options to see why they are incorrect.

Addition Property of Equality

The Addition Property of Equality states that if two expressions are equal, then we can add the same value to both sides of the equation without changing the equality. In this case, we have the equation $12 = x + 5$, and adding 5 to both sides would result in $17 = x + 10$, not $x + 5 = 12$.

Reflexive Property of Equality

The Reflexive Property of Equality states that every expression is equal to itself. In this case, we have the equation $12 = x + 5$, and the Reflexive Property does not apply because we are not comparing an expression to itself.

Subtraction Property of Equality

The Subtraction Property of Equality states that if two expressions are equal, then we can subtract the same value from both sides of the equation without changing the equality. In this case, we have the equation $12 = x + 5$, and subtracting 5 from both sides would result in $7 = x$, not $x + 5 = 12$.

Conclusion

In conclusion, the Symmetric Property of Equality justifies the given statement. The Symmetric Property states that if two expressions are equal, then their order can be reversed without changing the equality. This property is essential in solving equations and inequalities, and it helps us manipulate expressions to find the solution.

Final Answer

The final answer is:

  • B. Symmetric Property of Equality

References

  • [1] "Properties of Equality" by Math Open Reference
  • [2] "Symmetric Property of Equality" by Khan Academy
  • [3] "Reflexive Property of Equality" by Purplemath
  • [4] "Addition Property of Equality" by Mathway
  • [5] "Subtraction Property of Equality" by IXL
    Which Property Justifies This Statement? - Q&A =====================================================

Introduction

In our previous article, we explored the properties of equality and determined that the Symmetric Property of Equality justifies the given statement: If $12 = x + 5$, then $x + 5 = 12$. In this article, we will provide a Q&A section to help you better understand the properties of equality and how to apply them.

Q&A

Q: What is the Symmetric Property of Equality?

A: The Symmetric Property of Equality states that if two expressions are equal, then their order can be reversed without changing the equality. In other words, if $a = b$, then $b = a$.

Q: How does the Symmetric Property of Equality differ from the Reflexive Property of Equality?

A: The Reflexive Property of Equality states that every expression is equal to itself. In contrast, the Symmetric Property of Equality states that if two expressions are equal, then their order can be reversed without changing the equality.

Q: Can the Symmetric Property of Equality be used to justify the equation $x + 5 = 12$ if we start with the equation $12 = x + 5$?

A: Yes, the Symmetric Property of Equality can be used to justify the equation $x + 5 = 12$ if we start with the equation $12 = x + 5$. This is because the order of the expressions can be reversed without changing the equality.

Q: What is the Addition Property of Equality?

A: The Addition Property of Equality states that if two expressions are equal, then we can add the same value to both sides of the equation without changing the equality. In other words, if $a = b$, then $a + c = b + c$.

Q: Can the Addition Property of Equality be used to justify the equation $x + 5 = 12$ if we start with the equation $12 = x + 5$?

A: No, the Addition Property of Equality cannot be used to justify the equation $x + 5 = 12$ if we start with the equation $12 = x + 5$. This is because adding 5 to both sides would result in $17 = x + 10$, not $x + 5 = 12$.

Q: What is the Subtraction Property of Equality?

A: The Subtraction Property of Equality states that if two expressions are equal, then we can subtract the same value from both sides of the equation without changing the equality. In other words, if $a = b$, then $a - c = b - c$.

Q: Can the Subtraction Property of Equality be used to justify the equation $x + 5 = 12$ if we start with the equation $12 = x + 5$?

A: No, the Subtraction Property of Equality cannot be used to justify the equation $x + 5 = 12$ if we start with the equation $12 = x + 5$. This is because subtracting 5 from both sides would result in $7 = x$, not $x + 5 = 12$.

Conclusion

In conclusion, the Symmetric Property of Equality justifies the given statement: If $12 = x + 5$, then $x + 5 = 12$. The Symmetric Property states that if two expressions are equal, then their order can be reversed without changing the equality. This property is essential in solving equations and inequalities, and it helps us manipulate expressions to find the solution.

Final Answer

The final answer is:

  • B. Symmetric Property of Equality

References

  • [1] "Properties of Equality" by Math Open Reference
  • [2] "Symmetric Property of Equality" by Khan Academy
  • [3] "Reflexive Property of Equality" by Purplemath
  • [4] "Addition Property of Equality" by Mathway
  • [5] "Subtraction Property of Equality" by IXL