Select The Correct Answer.Hattie Rewrote The Equation As Shown:$\[ \begin{array}{l} 9n + 7 - 2n = 4(-n + 5) - 3n \\ 9n + 7 - 2n = -4n + 20 - 3n \end{array} \\]Which Property Did She Use To Rewrite The Equation?A. Addition Property Of Equality

Introduction

In mathematics, solving equations is a crucial skill that helps us find the value of unknown variables. When we have an equation with variables, we need to isolate the variable to find its value. One of the properties that helps us simplify equations is the Addition Property of Equality. In this article, we will explore the Addition Property of Equality, its definition, and how it is used to rewrite equations.

What is the Addition Property of Equality?

The Addition Property of Equality states that if we add the same value to both sides of an equation, the equation remains true. This property is also known as the Addition Property of Equality or the Addition Property. It is denoted by the following symbol: $\boxed{+}$.

Definition

The Addition Property of Equality can be defined as:

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

Example

Let's consider an example to illustrate the Addition Property of Equality. Suppose we have the equation:

$$x + 3 = 5$$

We can add 2 to both sides of the equation to get:

$$x + 3 + 2 = 5 + 2$$

This simplifies to:

$$x + 5 = 7$$

As we can see, the equation remains true after adding 2 to both sides.

How is the Addition Property of Equality Used to Rewrite Equations?

The Addition Property of Equality is used to rewrite equations by adding or subtracting the same value to both sides of the equation. This helps us simplify the equation and isolate the variable.

Example

Let's consider the equation:

$$9n + 7 - 2n = 4(-n + 5) - 3n$$

We can rewrite this equation by adding $2n$ to both sides:

$$9n + 7 - 2n + 2n = 4(-n + 5) - 3n + 2n$$

This simplifies to:

$$9n + 7 = 4(-n + 5) - n$$

We can further simplify the equation by adding $n$ to both sides:

$$9n + 7 + n = 4(-n + 5) - n + n$$

This simplifies to:

$$10n + 7 = 4(-n + 5)$$

As we can see, the equation remains true after adding $2n$ and $n$ to both sides.

Conclusion

In conclusion, the Addition Property of Equality is a fundamental property in mathematics that helps us simplify equations and isolate variables. By adding or subtracting the same value to both sides of an equation, we can rewrite the equation and make it easier to solve. The Addition Property of Equality is a powerful tool that helps us solve equations and understand the underlying mathematics.

Answer

Based on the equation provided, Hattie rewrote the equation as shown:

$$\begin{array}{l} 9n + 7 - 2n = 4(-n + 5) - 3n \\ 9n + 7 - 2n = -4n + 20 - 3n \end{array}$$

She used the Addition Property of Equality to rewrite the equation by adding $2n$ to both sides.

Final Answer

Q: What is the Addition Property of Equality?

A: The Addition Property of Equality states that if we add the same value to both sides of an equation, the equation remains true. This property is also known as the Addition Property of Equality or the Addition Property.

Q: How is the Addition Property of Equality used to rewrite equations?

A: The Addition Property of Equality is used to rewrite equations by adding or subtracting the same value to both sides of the equation. This helps us simplify the equation and isolate the variable.

Q: Can you provide an example of the Addition Property of Equality?

A: Let's consider the equation:

$$x + 3 = 5$$

We can add 2 to both sides of the equation to get:

$$x + 3 + 2 = 5 + 2$$

This simplifies to:

$$x + 5 = 7$$

As we can see, the equation remains true after adding 2 to both sides.

Q: What is the difference between the Addition Property of Equality and the Subtraction Property of Equality?

A: The Addition Property of Equality states that if we add the same value to both sides of an equation, the equation remains true. The Subtraction Property of Equality states that if we subtract the same value from both sides of an equation, the equation remains true.

Q: Can you provide an example of the Subtraction Property of Equality?

A: Let's consider the equation:

$$x + 2 = 7$$

We can subtract 2 from both sides of the equation to get:

$$x + 2 - 2 = 7 - 2$$

This simplifies to:

$$x = 5$$

As we can see, the equation remains true after subtracting 2 from both sides.

Q: How is the Addition Property of Equality used in real-life situations?

A: The Addition Property of Equality is used in many real-life situations, such as:

• Solving equations in physics and engineering
• Calculating interest rates and investments
• Determining the cost of goods and services
• Solving problems in computer science and programming

Q: Can you provide a real-life example of the Addition Property of Equality?

A: Let's consider a real-life example:

Suppose we have a bank account with a balance of $1000. We deposit $500 into the account. We can use the Addition Property of Equality to calculate the new balance:

$$1000 + 500 = 1500$$

As we can see, the equation remains true after adding 500 to both sides.

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 the wrong value to both sides of the equation
• Not simplifying the equation after adding or subtracting the value
• Not checking the equation for equality after adding or subtracting the value

Q: Can you provide a summary of the Addition Property of Equality?

A: The Addition Property of Equality states that if we add the same value to both sides of an equation, the equation remains true. This property is used to rewrite equations by adding or subtracting the same value to both sides of the equation. It is a fundamental property in mathematics that helps us simplify equations and isolate variables.