Select The Statement That Best Justifies The Conclusion Based On The Given Information.Given: X + Y = Z X + Y = Z X + Y = Z And X = Y X = Y X = Y Conclusion: X + X = Z X + X = Z X + X = Z A. Substitution B. Addition Property Of Equality C. Closure D. Additive Inverse

Introduction

In mathematics, conclusions are often drawn from given information using various properties and rules. However, it's essential to identify the correct justification for a particular conclusion. In this article, we will analyze a given statement and conclusion to determine the best justification based on the provided information.

Given Information

The given information is:

• $x + y = z$
• $x = y$

Conclusion

The conclusion drawn from the given information is:

$x + x = z$

Justification Options

We have four options to justify the conclusion:

A. Substitution B. Addition property of equality C. Closure D. Additive inverse

Analyzing the Options

A. Substitution

Substitution involves replacing a variable with an expression that is equal to it. In this case, we can substitute $y$ with $x$ in the equation $x + y = z$. This would give us $x + x = z$, which is the conclusion we are trying to justify.

However, we need to check if this substitution is valid. Since $x = y$, we can indeed substitute $y$ with $x$ in the equation. Therefore, substitution is a valid justification for the conclusion.

B. Addition property of equality

The addition property of equality states that if two expressions are equal, then their sum with the same expression is also equal. In this case, we have $x + y = z$, and we want to add $x$ to both sides of the equation.

However, the addition property of equality does not directly apply here. We are not adding $x$ to both sides of the equation; instead, we are substituting $y$ with $x$. Therefore, the addition property of equality is not the correct justification for the conclusion.

C. Closure

Closure refers to the property that the result of an operation is always within the same set. In this case, we are adding $x$ to itself, and the result is $z$. However, closure does not directly apply here, as we are not concerned with the set of values that $x$ and $z$ can take.

D. Additive inverse

The additive inverse of a number is the value that, when added to it, results in zero. In this case, we are not concerned with the additive inverse of $x$ or $z$. Therefore, the additive inverse is not the correct justification for the conclusion.

Conclusion

Based on the analysis of the options, we can conclude that the best justification for the conclusion $x + x = z$ is:

• A. Substitution

Substitution is the correct justification because we can substitute $y$ with $x$ in the equation $x + y = z$, resulting in $x + x = z$. This substitution is valid because $x = y$.

Final Answer

Introduction

In our previous article, we analyzed a given statement and conclusion to determine the best justification based on the provided information. In this article, we will address some frequently asked questions (FAQs) related to selecting the correct justification for a mathematical conclusion.

Q: What is the difference between substitution and addition property of equality?

A: Substitution involves replacing a variable with an expression that is equal to it, whereas the addition property of equality states that if two expressions are equal, then their sum with the same expression is also equal. In the context of the given information, substitution is the correct justification because we can substitute $y$ with $x$ in the equation $x + y = z$, resulting in $x + x = z$.

Q: Can I use the addition property of equality to justify the conclusion?

A: No, the addition property of equality does not directly apply here. We are not adding $x$ to both sides of the equation; instead, we are substituting $y$ with $x$. The addition property of equality would be relevant if we were adding $x$ to both sides of the equation, but that is not the case here.

Q: What is closure, and how does it relate to the given information?

A: Closure refers to the property that the result of an operation is always within the same set. In the context of the given information, we are adding $x$ to itself, and the result is $z$. However, closure does not directly apply here, as we are not concerned with the set of values that $x$ and $z$ can take.

Q: Can I use the additive inverse to justify the conclusion?

A: No, the additive inverse of a number is the value that, when added to it, results in zero. In the context of the given information, we are not concerned with the additive inverse of $x$ or $z$. The additive inverse is not relevant to justifying the conclusion.

Q: How do I determine the correct justification for a mathematical conclusion?

A: To determine the correct justification for a mathematical conclusion, you should:

1. Read the given information carefully and identify the key equations and relationships.
2. Analyze the conclusion and determine what operation or property is being used to arrive at the conclusion.
3. Check if the operation or property is valid and applicable to the given information.
4. Select the correct justification based on your analysis.

Q: What are some common pitfalls to avoid when selecting the correct justification for a mathematical conclusion?

A: Some common pitfalls to avoid when selecting the correct justification for a mathematical conclusion include:

1. Misinterpreting the given information or the conclusion.
2. Failing to analyze the operation or property being used to arrive at the conclusion.
3. Selecting a justification that is not valid or applicable to the given information.
4. Not considering alternative justifications or explanations.

Conclusion

In conclusion, selecting the correct justification for a mathematical conclusion requires careful analysis and attention to detail. By understanding the key concepts and properties involved, you can determine the correct justification and arrive at the correct conclusion. Remember to read the given information carefully, analyze the conclusion, and select the correct justification based on your analysis.