Identifying the Property Used

Oct 13, 2025 by magicalceylontours.com 31 views

Introduction

In the given solution, we are presented with a simple algebraic equation involving fractions. The equation is $\frac{7}{3} x = -2$ , and we are asked to find the value of $x$ . The solution provided involves multiplying both sides of the equation by a fraction, resulting in the value of $x$ being $-\frac{6}{7}$ . In this article, we will analyze the solution and identify the property used to solve the equation.

The Solution

The solution provided is as follows:

$\begin{array}{l} \frac{7}{3} x = -2 \\ \frac{7}{3} x \left(\frac{3}{7}\right) = -2 \left(\frac{3}{7}\right) \\ x = -\frac{6}{7} \end{array}$

Identifying the Property Used

To identify the property used to solve the equation, let's examine the steps involved in the solution. The first step involves multiplying both sides of the equation by $\frac{3}{7}$ . This is a crucial step, as it allows us to isolate the variable $x$ .

The Multiplication Property of Equality

The property used to solve the equation is the Multiplication Property of Equality. This property states that if we multiply both sides of an equation by the same non-zero value, the equation remains true.

In this case, we multiplied both sides of the equation by $\frac{3}{7}$ , which is a non-zero value. This allowed us to eliminate the fraction $\frac{7}{3}$ from the left-hand side of the equation, resulting in the value of $x$ being $-\frac{6}{7}$ .

The Importance of the Multiplication Property of Equality

The Multiplication Property of Equality is a fundamental concept in algebra, and it is used extensively in solving equations involving fractions. By understanding this property, we can solve equations involving fractions with ease.

Real-World Applications

The Multiplication Property of Equality has numerous real-world applications. For example, in finance, it is used to calculate interest rates and investments. In science, it is used to calculate the rate of change of a quantity. In engineering, it is used to design and optimize systems.

Conclusion

In conclusion, the solution provided involves the use of the Multiplication Property of Equality to solve the equation. By understanding this property, we can solve equations involving fractions with ease. The Multiplication Property of Equality has numerous real-world applications, and it is a fundamental concept in algebra.

Final Thoughts

The solution provided is a simple example of how the Multiplication Property of Equality can be used to solve equations involving fractions. However, it is essential to remember that this property can be used in more complex equations as well. By understanding this property, we can solve a wide range of equations and problems in various fields.

Additional Resources

For those who want to learn more about the Multiplication Property of Equality, there are numerous resources available online. Some recommended resources include:

Khan Academy: Multiplication Property of Equality
Mathway: Multiplication Property of Equality
Wolfram Alpha: Multiplication Property of Equality

Conclusion

Final Thoughts

Additional Resources

For those who want to learn more about the Multiplication Property of Equality, there are numerous resources available online. Some recommended resources include:

Khan Academy: Multiplication Property of Equality
Mathway: Multiplication Property of Equality
Wolfram Alpha: Multiplication Property of Equality

Conclusion

Final Thoughts

Additional Resources

For those who want to learn more about the Multiplication Property of Equality, there are numerous resources available online. Some recommended resources include:

Khan Academy: Multiplication Property of Equality
Mathway: Multiplication Property of Equality
Wolfram Alpha: Multiplication Property of Equality

Q: What is the Multiplication Property of Equality?

A: The Multiplication Property of Equality is a fundamental concept in algebra that states that if we multiply both sides of an equation by the same non-zero value, the equation remains true.

Q: Why is the Multiplication Property of Equality important?

A: The Multiplication Property of Equality is essential in solving equations involving fractions. By understanding this property, we can isolate the variable and solve for its value.

Q: Can the Multiplication Property of Equality be used in more complex equations?

A: Yes, the Multiplication Property of Equality can be used in more complex equations involving fractions, decimals, and other mathematical operations.

Q: What are some real-world applications of the Multiplication Property of Equality?

A: The Multiplication Property of Equality has numerous real-world applications in finance, science, engineering, and other fields. It is used to calculate interest rates, investments, rates of change, and system design.

Q: How can I apply the Multiplication Property of Equality in my daily life?

A: You can apply the Multiplication Property of Equality in your daily life by using it to solve problems involving fractions, decimals, and other mathematical operations. For example, you can use it to calculate the cost of an item, the interest rate on a loan, or the rate of change of a quantity.

Q: What are some common mistakes to avoid when using the Multiplication Property of Equality?

A: Some common mistakes to avoid when using the Multiplication Property of Equality include:

Multiplying both sides of the equation by a zero value, which results in an undefined equation.
Multiplying both sides of the equation by a negative value, which results in a change in the sign of the equation.
Failing to check if the equation is true before multiplying both sides by a value.

Q: How can I practice using the Multiplication Property of Equality?

A: You can practice using the Multiplication Property of Equality by solving equations involving fractions, decimals, and other mathematical operations. You can also use online resources, such as Khan Academy, Mathway, and Wolfram Alpha, to practice and learn more about the Multiplication Property of Equality.

Q: What are some additional resources for learning about the Multiplication Property of Equality?

A: Some additional resources for learning about the Multiplication Property of Equality include:

Khan Academy: Multiplication Property of Equality
Mathway: Multiplication Property of Equality
Wolfram Alpha: Multiplication Property of Equality
Algebra textbooks and online resources
Math tutoring services

Q: Can I use the Multiplication Property of Equality to solve equations involving variables on both sides?

A: Yes, the Multiplication Property of Equality can be used to solve equations involving variables on both sides. However, you must be careful to isolate the variable on one side of the equation before multiplying both sides by a value.

Q: What are some common applications of the Multiplication Property of Equality in finance?

A: Some common applications of the Multiplication Property of Equality in finance include:

Calculating interest rates on loans and investments
Determining the cost of an item or service
Calculating the rate of return on an investment
Determining the value of a stock or bond

Q: What are some common applications of the Multiplication Property of Equality in science?

A: Some common applications of the Multiplication Property of Equality in science include:

Calculating the rate of change of a quantity
Determining the value of a physical constant
Calculating the energy of a system
Determining the velocity of an object

Q: What are some common applications of the Multiplication Property of Equality in engineering?

A: Some common applications of the Multiplication Property of Equality in engineering include:

Designing and optimizing systems
Calculating the stress and strain on a material
Determining the value of a physical constant
Calculating the energy of a system

Q: Can I use the Multiplication Property of Equality to solve equations involving exponents?

A: Yes, the Multiplication Property of Equality can be used to solve equations involving exponents. However, you must be careful to apply the exponent rules correctly when multiplying both sides of the equation by a value.