Find Equivalent Expressions Of 3 + 2 X − 9 − 4 X + 11 + 5 X − X 3 + 2x - 9 - 4x + 11 + 5x - X 3 + 2 X − 9 − 4 X + 11 + 5 X − X .Choose Three Expressions.A. 2 X + 5 2x + 5 2 X + 5 B. 12 X + 23 12x + 23 12 X + 23 C. 3 X − 2 − X + 1 3x - 2 - X + 1 3 X − 2 − X + 1 D. 4 X + 11 − 2 X − 6 4x + 11 - 2x - 6 4 X + 11 − 2 X − 6 E. 2 X − 1 − 4 X + 4 2x - 1 - 4x + 4 2 X − 1 − 4 X + 4 F. $2x - X +

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on finding equivalent expressions of a given algebraic expression, which is a key concept in algebra. We will use the expression $3 + 2x - 9 - 4x + 11 + 5x - x$ as an example and choose three equivalent expressions from the given options.

Understanding Equivalent Expressions

Equivalent expressions are algebraic expressions that have the same value, but may be written in different ways. They can be obtained by adding, subtracting, multiplying, or dividing both sides of an equation by the same value. In other words, equivalent expressions are expressions that have the same solution or value.

Simplifying the Given Expression

To simplify the given expression $3 + 2x - 9 - 4x + 11 + 5x - x$, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are the terms with the variable $x$.

3 + 2x - 9 - 4x + 11 + 5x - x

We can start by combining the constant terms:

3 - 9 + 11 = 5

Next, we can combine the terms with the variable $x$:

2x - 4x + 5x - x = 2x

Now, we can rewrite the expression by combining the constant term and the term with the variable $x$:

5 + 2x

Choosing Equivalent Expressions

We are given six options for equivalent expressions, and we need to choose three of them. To do this, we need to compare the simplified expression $5 + 2x$ with each of the given options.

Option A: $2x + 5$

This option is equivalent to the simplified expression $5 + 2x$. We can see that the terms are in the same order, and the coefficients are the same.

Option B: $12x + 23$

This option is not equivalent to the simplified expression $5 + 2x$. The coefficient of the variable $x$ is different, and the constant term is also different.

Option C: $3x - 2 - x + 1$

This option is not equivalent to the simplified expression $5 + 2x$. The terms are not in the same order, and the coefficients are different.

Option D: $4x + 11 - 2x - 6$

This option is not equivalent to the simplified expression $5 + 2x$. The terms are not in the same order, and the coefficients are different.

Option E: $2x - 1 - 4x + 4$

This option is equivalent to the simplified expression $5 + 2x$. We can see that the terms are in the same order, and the coefficients are the same.

Option F: $2x - x + 5$

This option is equivalent to the simplified expression $5 + 2x$. We can see that the terms are in the same order, and the coefficients are the same.

Conclusion

In this article, we simplified the algebraic expression $3 + 2x - 9 - 4x + 11 + 5x - x$ and chose three equivalent expressions from the given options. We used the concept of like terms and combined them to simplify the expression. We also compared the simplified expression with each of the given options and chose the ones that were equivalent.

Final Answer

The three equivalent expressions are:

• Option A: $2x + 5$
• Option E: $2x - 1 - 4x + 4$
• Option F: $2x - x + 5$

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it can be a bit challenging for some students. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that does not change.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. You can combine like terms by adding or subtracting their coefficients.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, if you have the expression 2x + 4x, you can combine the like terms by adding their coefficients: 2x + 4x = 6x.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an algebraic expression. The order of operations is:

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.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to evaluate the expression inside the parentheses first. Then, you can simplify the expression outside the parentheses.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical statement that contains variables and constants, while an equation is a mathematical statement that contains an equal sign (=) and two expressions that are equal.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Conclusion

In this article, we answered some frequently asked questions about simplifying algebraic expressions. We covered topics such as like terms, combining like terms, the order of operations, and solving equations. We hope that this article has been helpful in clarifying any confusion you may have had about simplifying algebraic expressions.

Final Tips

• Always read the problem carefully and understand what is being asked.
• Use the order of operations to simplify expressions.
• Combine like terms to simplify expressions.
• Solve equations by isolating the variable on one side of the equation.

By following these tips, you should be able to simplify algebraic expressions with ease.