Select The Correct Answer. The Given Equation Has Been Solved In The Table. Step Statement 1 2/3x - 9 = -13 2 2/3x - 9 + 9 = -13 + 9 3 2/3x = -4 4 3/2 . 2/3x = 3/2 . (-4) 5 X = -6 In Which Step Was The Addition Property Of Equality Applied? A.step

by ADMIN 248 views

Select the Correct Answer: Understanding the Addition Property of Equality

The addition property of equality is a fundamental concept in algebra that states if two expressions are equal, then adding the same value to both sides of the equation will result in two new expressions that are also equal. This property is essential in solving equations and is used extensively in various mathematical operations. In this article, we will explore the addition property of equality and identify the step where it is applied in a given equation.

Understanding the Addition Property of Equality

The addition property of equality can be stated as follows:

If a = b, then a + c = b + c

This means that if two expressions are equal, adding the same value to both sides of the equation will result in two new expressions that are also equal.

Analyzing the Given Equation

The given equation is:

2/3x - 9 = -13

We are asked to identify the step where the addition property of equality is applied. Let's analyze the steps in the table:

Step 1: 2/3x - 9 = -13

In this step, we are given the original equation.

Step 2: 2/3x - 9 + 9 = -13 + 9

In this step, we add 9 to both sides of the equation. This is an example of the addition property of equality, where we add the same value to both sides of the equation.

Step 3: 2/3x = -4

In this step, we simplify the equation by combining like terms.

Step 4: 3/2 . 2/3x = 3/2 . (-4)

In this step, we multiply both sides of the equation by a fraction.

Step 5: x = -6

In this step, we solve for x by dividing both sides of the equation by the fraction.

Identifying the Step Where the Addition Property of Equality is Applied

Based on our analysis, we can see that the addition property of equality is applied in Step 2, where we add 9 to both sides of the equation.

In conclusion, the addition property of equality is a fundamental concept in algebra that states if two expressions are equal, then adding the same value to both sides of the equation will result in two new expressions that are also equal. In the given equation, the addition property of equality is applied in Step 2, where we add 9 to both sides of the equation.

The correct answer is Step 2.

The addition property of equality is a crucial concept in algebra that is used extensively in various mathematical operations. It is essential to understand this property to solve equations and manipulate expressions. In this article, we analyzed the given equation and identified the step where the addition property of equality is applied. We hope this article has provided valuable insights into the addition property of equality and its application in solving equations.
Q&A: Addition Property of Equality

In our previous article, we explored the addition property of equality and identified the step where it is applied in a given equation. In this article, we will answer some frequently asked questions about the addition property of equality.

Q: What is the addition property of equality?

A: The addition property of equality states that if two expressions are equal, then adding the same value to both sides of the equation will result in two new expressions that are also equal.

Q: Why is the addition property of equality important?

A: The addition property of equality is essential in solving equations and manipulating expressions. It allows us to add or subtract the same value from both sides of an equation, making it easier to solve for variables.

Q: How is the addition property of equality used in real-life situations?

A: The addition property of equality is used extensively in various real-life situations, such as:

  • Solving equations in physics and engineering
  • Calculating costs and profits in business
  • Determining the value of unknown quantities in finance
  • Solving problems in computer science and programming

Q: Can the addition property of equality be used with other mathematical operations?

A: Yes, the addition property of equality can be used with other mathematical operations, such as multiplication and division. However, it is essential to follow the order of operations and apply the correct property of equality for each operation.

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

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

  • Adding or subtracting different values from both sides of the equation
  • Failing to simplify the equation after applying the addition property of equality
  • Not following the order of operations

Q: How can I practice using the addition property of equality?

A: You can practice using the addition property of equality by:

  • Solving equations with variables
  • Manipulating expressions with variables
  • Using online resources and practice problems
  • Working with a tutor or teacher to review and practice the concept

Q: What are some real-world examples of the addition property of equality?

A: Some real-world examples of the addition property of equality include:

  • A company has a profit of $100,000 and wants to add a new product that will increase the profit by $20,000. Using the addition property of equality, we can calculate the new profit as $120,000.
  • A person has a savings account with a balance of $5,000 and wants to add a new deposit of $2,000. Using the addition property of equality, we can calculate the new balance as $7,000.

In conclusion, the addition property of equality is a fundamental concept in algebra that is used extensively in various mathematical operations. By understanding and applying this property, we can solve equations and manipulate expressions with ease. We hope this Q&A article has provided valuable insights into the addition property of equality and its application in real-life situations.