Select The Property Of Equality Used To Arrive At The Conclusion.If X − 3 = 7 X - 3 = 7 X − 3 = 7 , Then X = 10 X = 10 X = 10 .A. The Division Property Of Equality B. The Multiplication Property Of Equality C. The Addition Property Of Equality

Introduction

In mathematics, solving linear equations is a fundamental concept that involves manipulating algebraic expressions to isolate the variable. One of the key properties of equality is the ability to add, subtract, multiply, or divide both sides of an equation to maintain the equality. In this article, we will explore the properties of equality and determine which property is used to arrive at the conclusion in the given equation $x - 3 = 7$, then $x = 10$.

Understanding the Properties of Equality

There are four main properties of equality: addition, subtraction, multiplication, and division. These properties allow us to manipulate the equations to isolate the variable and solve for its value.

Addition Property of Equality

The addition property of equality states that if $a = b$, then $a + c = b + c$. This means that we can add the same value to both sides of an equation without changing the equality.

Subtraction Property of Equality

The subtraction property of equality states that if $a = b$, then $a - c = b - c$. This means that we can subtract the same value from both sides of an equation without changing the equality.

Multiplication Property of Equality

The multiplication property of equality states that if $a = b$, then $ac = bc$. This means that we can multiply both sides of an equation by the same non-zero value without changing the equality.

Division Property of Equality

The division property of equality states that if $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. This means that we can divide both sides of an equation by the same non-zero value without changing the equality.

Solving the Given Equation

Now that we have a good understanding of the properties of equality, let's apply them to the given equation $x - 3 = 7$, then $x = 10$.

Step 1: Add 3 to Both Sides

To isolate the variable $x$, we need to get rid of the constant term $-3$. We can do this by adding $3$ to both sides of the equation.

$x - 3 + 3 = 7 + 3$

This simplifies to:

$x = 10$

Step 2: Identify the Property Used

In the previous step, we added $3$ to both sides of the equation. This is an example of the addition property of equality.

Conclusion

In conclusion, the property of equality used to arrive at the conclusion in the given equation $x - 3 = 7$, then $x = 10$ is the addition property of equality. This property allows us to add the same value to both sides of an equation without changing the equality.

Answer

The correct answer is:

A. the addition property of equality

Final Thoughts

Introduction

In our previous article, we explored the properties of equality and determined which property is used to arrive at the conclusion in the given equation $x - 3 = 7$, then $x = 10$. In this article, we will answer some frequently asked questions (FAQs) about the properties of equality.

Q&A

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 we can add the same value to both sides of an equation without changing the equality.

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 we can subtract the same value from both sides of an equation without changing the equality.

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 we can multiply both sides of an equation by the same non-zero value without changing the equality.

Q: What is the division property of equality?

A: The division property of equality states that if $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. This means that we can divide both sides of an equation by the same non-zero value without changing the equality.

Q: Can I add or subtract any value to both sides of an equation?

A: No, you can only add or subtract the same value to both sides of an equation. If you add or subtract different values, you will change the equality.

Q: Can I multiply or divide both sides of an equation by any value?

A: No, you can only multiply or divide both sides of an equation by a non-zero value. If you multiply or divide by zero, you will change the equality.

Q: What happens if I add or subtract a negative value to both sides of an equation?

A: If you add or subtract a negative value to both sides of an equation, you will change the sign of the value. For example, if you add $-3$ to both sides of an equation, you will get $x + 3 = 7$.

Q: Can I use the properties of equality to solve equations with variables on both sides?

A: Yes, you can use the properties of equality to solve equations with variables on both sides. You can add or subtract the same value to both sides of the equation to isolate the variable.

Q: What is the order of operations when using the properties of equality?

A: When using the properties of equality, you should follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Conclusion

In conclusion, the properties of equality are fundamental concepts in mathematics that allow us to manipulate algebraic expressions to isolate the variable. By understanding the properties of equality, we can solve equations and inequalities with ease. In this article, we answered some frequently asked questions (FAQs) about the properties of equality.

Final Thoughts

The properties of equality are essential tools for solving equations and inequalities. By mastering the properties of equality, you will be able to solve a wide range of mathematical problems with confidence. Remember to always follow the order of operations and to use the properties of equality to isolate the variable.