Select The Property Of Equality Used To Arrive At The Conclusion.If 1 3 X = 5 \frac{1}{3} X = 5 3 1 ​ X = 5 , Then X = 15 X = 15 X = 15 .A. The Subtraction Property Of Equality B. The Multiplication Property Of Equality C. The Addition Property Of Equality

Introduction

In mathematics, the properties of equality are fundamental concepts that help us solve equations and maintain the balance of an equation. These properties are essential in algebra and are used to manipulate equations to isolate the variable. In this article, we will discuss the properties of equality and how they are used to arrive at a conclusion.

The Properties of Equality

There are three main properties of equality: the addition property of equality, the subtraction property of equality, and the multiplication property of equality. Each of these properties states that if two expressions are equal, then we can perform a specific operation on both sides of the equation without changing the equality.

The Addition Property of Equality

The addition property of equality states that if $a = b$, then $a + c = b + c$. This means that if we add the same value to both sides of an equation, the equality remains true.

Example 1: If $x = 5$, then $x + 3 = 5 + 3$

In this example, we added 3 to both sides of the equation, and the equality remains true.

The Subtraction Property of Equality

The subtraction property of equality states that if $a = b$, then $a - c = b - c$. This means that if we subtract the same value from both sides of an equation, the equality remains true.

Example 2: If $x = 5$, then $x - 3 = 5 - 3$

In this example, we subtracted 3 from both sides of the equation, and the equality remains true.

The Multiplication Property of Equality

The multiplication property of equality states that if $a = b$, then $ac = bc$. This means that if we multiply both sides of an equation by the same value, the equality remains true.

Example 3: If $x = 5$, then $3x = 3(5)$

In this example, we multiplied both sides of the equation by 3, and the equality remains true.

The Given Problem

The given problem is $\frac{1}{3} x = 5$, and we need to find the value of $x$. To solve this problem, we will use the multiplication property of equality.

Solution

To solve the problem, we need to isolate the variable $x$. We can do this by multiplying both sides of the equation by 3.

$\frac{1}{3} x = 5$

Multiplying both sides by 3:

$3(\frac{1}{3} x) = 3(5)$

Using the distributive property, we get:

$x = 15$

Therefore, the value of $x$ is 15.

Conclusion

In this article, we discussed the properties of equality and how they are used to arrive at a conclusion. We also solved a problem using the multiplication property of equality. The properties of equality are essential in mathematics and are used to manipulate equations to isolate the variable.

Answer

The correct answer is B. The multiplication property of equality.

References

• [1] "Algebra" by Michael Artin
• [2] "Mathematics for the Nonmathematician" by Morris Kline
  Frequently Asked Questions (FAQs) on the Properties of Equality ====================================================================

Introduction

In our previous article, we discussed the properties of equality and how they are used to arrive at a conclusion. In this article, we will answer some frequently asked questions (FAQs) on the properties of equality.

Q&A

Q: What is the addition property of equality?

A: The addition property of equality states that if $a = b$, then $a + c = b + c$. This means that if we add the same value to both sides of an equation, the equality remains true.

Q: What is the subtraction property of equality?

A: The subtraction property of equality states that if $a = b$, then $a - c = b - c$. This means that if we subtract the same value from both sides of an equation, the equality remains true.

Q: What is the multiplication property of equality?

A: The multiplication property of equality states that if $a = b$, then $ac = bc$. This means that if we multiply both sides of an equation by the same value, the equality remains true.

Q: Can I use the properties of equality to add or subtract the same value from both sides of an equation?

A: Yes, you can use the properties of equality to add or subtract the same value from both sides of an equation. For example, if $x = 5$, then $x + 3 = 5 + 3$ or $x - 3 = 5 - 3$.

Q: Can I use the properties of equality to multiply both sides of an equation by the same value?

A: Yes, you can use the properties of equality to multiply both sides of an equation by the same value. For example, if $x = 5$, then $3x = 3(5)$.

Q: What is the purpose of the properties of equality?

A: The properties of equality are used to manipulate equations to isolate the variable. They help us to solve equations and maintain the balance of an equation.

Q: Can I use the properties of equality to divide both sides of an equation by the same value?

A: Yes, you can use the properties of equality to divide both sides of an equation by the same value. However, you need to be careful when dividing both sides of an equation by a variable. For example, if $x = 5$, then $\frac{x}{3} = \frac{5}{3}$.

Q: What is the difference between the properties of equality and the properties of inequality?

A: The properties of equality and the properties of inequality are two different concepts in mathematics. The properties of equality are used to manipulate equations to isolate the variable, while the properties of inequality are used to compare two expressions.

Q: Can I use the properties of equality to solve equations with fractions?

A: Yes, you can use the properties of equality to solve equations with fractions. For example, if $\frac{1}{3} x = 5$, then you can multiply both sides of the equation by 3 to get $x = 15$.

Q: Can I use the properties of equality to solve equations with decimals?

A: Yes, you can use the properties of equality to solve equations with decimals. For example, if $x = 5.5$, then you can multiply both sides of the equation by 2 to get $2x = 11$.

Conclusion

In this article, we answered some frequently asked questions (FAQs) on the properties of equality. We hope that this article has helped you to understand the properties of equality and how they are used to arrive at a conclusion.

References

• [1] "Algebra" by Michael Artin
• [2] "Mathematics for the Nonmathematician" by Morris Kline