The First Step To Solve The Equation X 4 − 3 4 = 16 \frac{x}{4} - \frac{3}{4} = 16 4 X ​ − 4 3 ​ = 16 Is Shown Below. X 4 − 3 4 + 3 4 = 16 + 3 4 \frac{x}{4} - \frac{3}{4} + \frac{3}{4} = 16 + \frac{3}{4} 4 X ​ − 4 3 ​ + 4 3 ​ = 16 + 4 3 ​ Which Property Was Applied In This Step?A. Addition Property Of Equality B. Subtraction

The First Step to Solving Equations: Understanding the Addition Property of Equality

When it comes to solving equations, the first step often involves manipulating the equation to isolate the variable. In the given equation $\frac{x}{4} - \frac{3}{4} = 16$, the first step is to add $\frac{3}{4}$ to both sides of the equation. This step is crucial in understanding the property that was applied. In this article, we will explore the Addition Property of Equality and how it is used to solve equations.

What is the Addition Property of Equality?

The Addition Property of Equality states that if two expressions are equal, then adding the same value to both expressions will result in two new expressions that are also equal. This property can be expressed mathematically as:

$a = b$

$a + c = b + c$

where $a$, $b$, and $c$ are any real numbers.

Applying the Addition Property of Equality

In the given equation $\frac{x}{4} - \frac{3}{4} = 16$, the first step is to add $\frac{3}{4}$ to both sides of the equation. This can be written as:

$\frac{x}{4} - \frac{3}{4} + \frac{3}{4} = 16 + \frac{3}{4}$

By applying the Addition Property of Equality, we can see that the left-hand side of the equation becomes:

$\frac{x}{4} = 16 + \frac{3}{4}$

This is because adding $\frac{3}{4}$ to both sides of the equation results in two new expressions that are equal.

Why is the Addition Property of Equality Important?

The Addition Property of Equality is a fundamental concept in algebra and is used extensively in solving equations. It allows us to manipulate the equation to isolate the variable, making it easier to solve. By adding or subtracting the same value to both sides of the equation, we can create new expressions that are equal, which can then be used to solve for the variable.

Real-World Applications of the Addition Property of Equality

The Addition Property of Equality has numerous real-world applications. In finance, for example, it can be used to calculate the total cost of an item by adding the cost of the item to the cost of any additional fees or taxes. In science, it can be used to calculate the total amount of a substance by adding the amount of the substance to the amount of any impurities.

Conclusion

In conclusion, the Addition Property of Equality is a fundamental concept in algebra that is used extensively in solving equations. By adding or subtracting the same value to both sides of the equation, we can create new expressions that are equal, which can then be used to solve for the variable. Understanding the Addition Property of Equality is crucial in solving equations and has numerous real-world applications.

Example Problems

1. Solve the equation $2x + 5 = 11$ using the Addition Property of Equality.
2. Solve the equation $\frac{y}{3} - 2 = 4$ using the Addition Property of Equality.
3. Solve the equation $x - 3 = 7$ using the Addition Property of Equality.

Answer Key

1. $2x + 5 + (-5) = 11 + (-5)$ $2x = 6$ $x = 3$
2. $\frac{y}{3} - 2 + 2 = 4 + 2$ $\frac{y}{3} = 6$ $y = 18$
3. $x - 3 + 3 = 7 + 3$ $x = 10$

Practice Problems

1. Solve the equation $x + 2 = 9$ using the Addition Property of Equality.
2. Solve the equation $\frac{y}{2} + 3 = 5$ using the Addition Property of Equality.
3. Solve the equation $x - 2 = 6$ using the Addition Property of Equality.

Answer Key

1. $x + 2 + (-2) = 9 + (-2)$ $x = 7$
2. $\frac{y}{2} + 3 + (-3) = 5 + (-3)$ $\frac{y}{2} = 2$ $y = 4$
3. $x - 2 + 2 = 6 + 2$ $x = 8$
   Frequently Asked Questions: The Addition Property of Equality

In this article, we will answer some of the most 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 expressions will result in two new expressions that are also equal.

Q: How is the Addition Property of Equality used in solving equations?

A: The Addition Property of Equality is used to manipulate the equation to isolate the variable. By adding or subtracting the same value to both sides of the equation, we can create new expressions that are equal, which can then be used to solve for the variable.

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 two expressions are equal, then adding the same value to both expressions will result in two new expressions that are also equal. The Subtraction Property of Equality states that if two expressions are equal, then subtracting the same value from both expressions will result in two new expressions that are also equal.

Q: Can the Addition Property of Equality be used to solve equations with fractions?

A: Yes, the Addition Property of Equality can be used to solve equations with fractions. When working with fractions, it is essential to add or subtract the same value to both sides of the equation.

Q: How do I know when to use the Addition Property of Equality?

A: You should use the Addition Property of Equality when you need to add a value to both sides of the equation to isolate the variable. This is often the case when the variable is being added or subtracted from a constant.

Q: Can the Addition Property of Equality be used to solve equations with decimals?

A: Yes, the Addition Property of Equality can be used to solve equations with decimals. When working with decimals, it is essential to add or subtract the same value to both sides of the equation.

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

A: The Addition Property of Equality has numerous real-world applications. In finance, for example, it can be used to calculate the total cost of an item by adding the cost of the item to the cost of any additional fees or taxes. In science, it can be used to calculate the total amount of a substance by adding the amount of the substance to the amount of any impurities.

Q: Can the Addition Property of Equality be used to solve equations with variables on both sides?

A: Yes, the Addition Property of Equality can be used to solve equations with variables on both sides. When working with equations that have variables on both sides, it is essential to add or subtract the same value to both sides of the equation to isolate the variable.

Q: How do I know when to use the Addition Property of Equality versus the Subtraction Property of Equality?

A: You should use the Addition Property of Equality when you need to add a value to both sides of the equation to isolate the variable. You should use the Subtraction Property of Equality when you need to subtract a value from both sides of the equation to isolate the variable.

Q: Can the Addition Property of Equality be used to solve equations with negative numbers?

A: Yes, the Addition Property of Equality can be used to solve equations with negative numbers. When working with negative numbers, it is essential to add or subtract the same value to both sides of the equation.

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 isolating the variable
• Not checking the solution to ensure it is correct

Conclusion

In conclusion, the Addition Property of Equality is a fundamental concept in algebra that is used extensively in solving equations. By understanding the Addition Property of Equality, you can manipulate the equation to isolate the variable and solve for the unknown. Remember to use the Addition Property of Equality when you need to add a value to both sides of the equation to isolate the variable.

Practice Problems

1. Solve the equation $x + 2 = 9$ using the Addition Property of Equality.
2. Solve the equation $\frac{y}{2} + 3 = 5$ using the Addition Property of Equality.
3. Solve the equation $x - 2 = 6$ using the Addition Property of Equality.

Answer Key

1. $x + 2 + (-2) = 9 + (-2)$ $x = 7$
2. $\frac{y}{2} + 3 + (-3) = 5 + (-3)$ $\frac{y}{2} = 2$ $y = 4$
3. $x - 2 + 2 = 6 + 2$ $x = 8$