Which Property Of Equality Should Wade Use To Solve The Equation $\frac{x}{6} = 3$?A. Addition Property Of Equality B. Subtraction Property Of Equality C. Multiplication Property Of Equality D. Distributive Property Of Equality

Feb 26, 2025 by ADMIN 233 views

**Solving Equations with the Properties of Equality**

Introduction

In mathematics, equations are a fundamental concept that helps us solve problems and understand relationships between variables. When solving equations, we often use various properties of equality to manipulate the equation and isolate the variable. In this article, we will explore which property of equality Wade should use to solve the equation $\frac{x}{6} = 3$ .

Understanding the Properties of Equality

Before we dive into the solution, let's briefly review the properties of equality. There are four main properties of equality:

Addition Property of Equality: If $a = b$ , then $a + c = b + c$ .
Subtraction Property of Equality: If $a = b$ , then $a - c = b - c$ .
Multiplication Property of Equality: If $a = b$ , then $ac = bc$ .
Distributive Property of Equality: If $a = b$ , then $a(c + d) = bc + bd$ .

Analyzing the Given Equation

The given equation is $\frac{x}{6} = 3$ . To solve for $x$ , we need to isolate the variable $x$ . Let's analyze the equation and determine which property of equality we can use to solve it.

Using the Multiplication Property of Equality

To solve the equation $\frac{x}{6} = 3$ , we can use the multiplication property of equality. This property states that if $a = b$ , then $ac = bc$ . In this case, we can multiply both sides of the equation by 6 to eliminate the fraction.

$\frac{x}{6} = 3$

Multiplying both sides by 6:

$x = 3 \times 6$

$x = 18$

Therefore, the value of $x$ is 18.

Conclusion

In conclusion, Wade should use the multiplication property of equality to solve the equation $\frac{x}{6} = 3$ . This property allows us to eliminate the fraction and isolate the variable $x$ . By multiplying both sides of the equation by 6, we can easily solve for $x$ and find the value of 18.

Why the Other Options are Incorrect

Let's briefly discuss why the other options are incorrect:

Addition Property of Equality: This property is not applicable in this case, as we are not adding any values to the equation.
Subtraction Property of Equality: This property is also not applicable, as we are not subtracting any values from the equation.
Distributive Property of Equality: This property is not relevant in this case, as we are not distributing any values to the equation.

Real-World Applications

Solving equations with the properties of equality has numerous real-world applications. For example, in finance, we use equations to calculate interest rates and investments. In science, we use equations to model physical phenomena and make predictions. In engineering, we use equations to design and optimize systems.

Tips and Tricks

Here are some tips and tricks to help you solve equations with the properties of equality:

Read the equation carefully: Before solving the equation, read it carefully and identify the variable you need to isolate.
Choose the correct property: Select the property of equality that is most relevant to the equation.
Simplify the equation: Simplify the equation as much as possible to make it easier to solve.
Check your answer: Once you have solved the equation, check your answer to ensure it is correct.

Conclusion

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 two values are equal, adding the same value to both sides will not change the equality.

Q: How do I use the addition property of equality to solve an equation?

A: To use the addition property of equality, identify the value you need to add to both sides of the equation to isolate the variable. Then, add that value to both sides of the equation.

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 two values are equal, subtracting the same value from both sides will not change the equality.

Q: How do I use the subtraction property of equality to solve an equation?

A: To use the subtraction property of equality, identify the value you need to subtract from both sides of the equation to isolate the variable. Then, subtract that value from both sides of the equation.

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 two values are equal, multiplying both sides by the same value will not change the equality.

Q: How do I use the multiplication property of equality to solve an equation?

A: To use the multiplication property of equality, identify the value you need to multiply both sides of the equation by to isolate the variable. Then, multiply both sides of the equation by that value.

Q: What is the distributive property of equality?

A: The distributive property of equality states that if $a = b$ , then $a(c + d) = bc + bd$ . This means that if two values are equal, you can distribute the same value to both sides of the equation without changing the equality.

Q: How do I use the distributive property of equality to solve an equation?

A: To use the distributive property of equality, identify the value you need to distribute to both sides of the equation to isolate the variable. Then, distribute that value to both sides of the equation.

Q: What are some common mistakes to avoid when using the properties of equality?

A: Some common mistakes to avoid when using the properties of equality include:

Adding or subtracting the wrong value to both sides of the equation
Multiplying or dividing both sides of the equation by the wrong value
Not checking the solution to ensure it is correct

Q: How do I know which property of equality to use when solving an equation?

A: To determine which property of equality to use, read the equation carefully and identify the variable you need to isolate. Then, choose the property of equality that is most relevant to the equation.

Q: Can I use more than one property of equality to solve an equation?

A: Yes, you can use more than one property of equality to solve an equation. In fact, often you will need to use multiple properties of equality to isolate the variable.

Q: What are some real-world applications of the properties of equality?

A: The properties of equality have numerous real-world applications, including:

Finance: Using equations to calculate interest rates and investments
Science: Using equations to model physical phenomena and make predictions
Engineering: Using equations to design and optimize systems

Q: How can I practice using the properties of equality to solve equations?

A: You can practice using the properties of equality to solve equations by working through example problems and exercises. You can also use online resources and practice tests to help you improve your skills.