Find Equivalent Expressions For 2 Y + 7 − 5 Y + 6 Y − 3 + Y 2y + 7 - 5y + 6y - 3 + Y 2 Y + 7 − 5 Y + 6 Y − 3 + Y . Choose Three Expressions.A. 14 Y − 10 + 4 14y - 10 + 4 14 Y − 10 + 4 B. − 4 Y − 4 -4y - 4 − 4 Y − 4 C. 3 Y + 4 + 2 Y 3y + 4 + 2y 3 Y + 4 + 2 Y D. 4 Y − 1 + 2 Y − Y − Y + 1 + 4 4y - 1 + 2y - Y - Y + 1 + 4 4 Y − 1 + 2 Y − Y − Y + 1 + 4 E. 9 Y − 5 + 9 − 5 Y 9y - 5 + 9 - 5y 9 Y − 5 + 9 − 5 Y F.

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 for a given algebraic expression. We will use the expression $2y + 7 - 5y + 6y - 3 + y$ 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 forms. They can be obtained by adding, subtracting, multiplying, or dividing the same value to each term in the original expression. In other words, equivalent expressions are expressions that have the same numerical value, but may be written in a different way.

Step 1: Simplify the Given Expression

To simplify the given expression $2y + 7 - 5y + 6y - 3 + y$, 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 $y$.

2y - 5y + 6y + y = 4y

Now, we can rewrite the expression as:

4y + 7 - 3

Next, we can combine the constant terms:

4y + 4

Step 2: Choose Equivalent Expressions

Now that we have simplified the given expression, we can choose three equivalent expressions from the given options. To do this, we need to look for expressions that have the same value as the simplified expression.

Option A: $14y - 10 + 4$

Let's simplify this expression:

14y - 10 + 4 = 14y - 6

This expression is not equivalent to the simplified expression $4y + 4$.

Option B: $-4y - 4$

Let's simplify this expression:

-4y - 4 = -4y - 4

This expression is not equivalent to the simplified expression $4y + 4$.

Option C: $3y + 4 + 2y$

Let's simplify this expression:

3y + 4 + 2y = 5y + 4

This expression is not equivalent to the simplified expression $4y + 4$.

Option D: $4y - 1 + 2y - y - y + 1 + 4$

Let's simplify this expression:

4y - 1 + 2y - y - y + 1 + 4 = 4y + 2y - 2y - 1 + 1 + 4
= 4y + 4

This expression is equivalent to the simplified expression $4y + 4$.

Option E: $9y - 5 + 9 - 5y$

Let's simplify this expression:

9y - 5 + 9 - 5y = 4y + 4

This expression is equivalent to the simplified expression $4y + 4$.

Option F: Not Provided

Since Option F is not provided, we cannot choose it as an equivalent expression.

Conclusion

In this article, we simplified the given algebraic expression $2y + 7 - 5y + 6y - 3 + y$ and chose three equivalent expressions from the given options. We found that Options D and E are equivalent to the simplified expression $4y + 4$. We also learned that equivalent expressions are algebraic expressions that have the same value, but may be written in different forms.

Tips and Tricks

• When simplifying algebraic expressions, always combine like terms first.
• When choosing equivalent expressions, look for expressions that have the same value as the simplified expression.
• Always check your work by plugging in values for the variables to ensure that the expressions are equivalent.

Practice Problems

1. Simplify the expression $3x + 2 - 2x + 4x - 1$.
2. Choose three equivalent expressions from the given options for the expression $2x - 3 + 4x - 2x + 1$.
3. Simplify the expression $5y - 2 + 3y + 2y - 1$.

Answer Key

1. $6x + 1$
2. Options A, C, and E are equivalent expressions.
3. $8y - 1$
   Frequently Asked Questions: 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 is a like term?

A: A like term is a term that has 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 choose equivalent expressions?

A: To choose equivalent expressions, you need to look for expressions that have the same value as the original expression. You can do this by simplifying the original expression and then looking for expressions that have the same value.

Q: What is an equivalent expression?

A: An equivalent expression is an algebraic expression that has the same value as the original expression, but may be written in a different form.

Q: How do I check if two expressions are equivalent?

A: To check if two expressions are equivalent, you can plug in values for the variables and see if the expressions have the same value.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Not combining like terms
• Not following the order of operations
• Not checking if the expressions are equivalent

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working through practice problems and checking your answers with a calculator or by plugging in values for the variables.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

• Solving systems of equations
• Finding the area and perimeter of shapes
• Modeling population growth and decay
• Solving optimization problems

Conclusion

Simplifying algebraic expressions is an important skill to master in mathematics. By understanding the concepts of like terms, the order of operations, and equivalent expressions, you can simplify complex algebraic expressions and solve a wide range of problems. Remember to practice regularly and check your answers to ensure that you are simplifying expressions correctly.