Select All Expressions That Are Equivalent To 6 X + 1 − ( 3 X − 1 6x + 1 - (3x - 1 6 X + 1 − ( 3 X − 1 ].A. 6 X + 1 − 3 X − 1 6x + 1 - 3x - 1 6 X + 1 − 3 X − 1 B. 6 X + ( − 3 X ) + 1 + 1 6x + (-3x) + 1 + 1 6 X + ( − 3 X ) + 1 + 1 C. 3 X + 2 3x + 2 3 X + 2 D. 6 X − 3 X + 1 − 1 6x - 3x + 1 - 1 6 X − 3 X + 1 − 1 E. 6 X + 1 + ( − 3 X ) − 1 6x + 1 + (-3x) - 1 6 X + 1 + ( − 3 X ) − 1 Justify Your Choice(s):

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on simplifying expressions that involve parentheses and like terms. We will use the given expression $6x + 1 - (3x - 1)$ as an example and explore the different ways to simplify it.

Understanding the Expression

The given expression is $6x + 1 - (3x - 1)$. To simplify this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: $3x - 1$
2. Simplify the expression by combining like terms

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is $3x - 1$. To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Multiply $3x$ by $-1$: $-3x$
2. Subtract $1$ from the result: $-3x - 1$

So, the expression inside the parentheses is $-3x - 1$.

Step 2: Simplify the Expression

Now that we have evaluated the expression inside the parentheses, we can simplify the original expression:

$6x + 1 - (3x - 1)$

Substitute the evaluated expression inside the parentheses:

$6x + 1 - (-3x - 1)$

Distribute the negative sign:

$6x + 1 + 3x + 1$

Combine like terms:

$9x + 2$

Comparing the Simplified Expression with the Options

Now that we have simplified the expression, let's compare it with the given options:

A. $6x + 1 - 3x - 1$ B. $6x + (-3x) + 1 + 1$ C. $3x + 2$ D. $6x - 3x + 1 - 1$ E. $6x + 1 + (-3x) - 1$

The simplified expression is $9x + 2$. Let's analyze each option:

• Option A: $6x + 1 - 3x - 1$ is equivalent to $3x$, not $9x + 2$.
• Option B: $6x + (-3x) + 1 + 1$ is equivalent to $3x + 2$, not $9x + 2$.
• Option C: $3x + 2$ is equivalent to the simplified expression, but it is not the only correct option.
• Option D: $6x - 3x + 1 - 1$ is equivalent to $3x$, not $9x + 2$.
• Option E: $6x + 1 + (-3x) - 1$ is equivalent to $3x$, not $9x + 2$.

Conclusion

In conclusion, the simplified expression $9x + 2$ is equivalent to option C, $3x + 2$. However, we can also rewrite the simplified expression as $6x + 1 - (3x - 1)$, which is equivalent to option A. Therefore, the correct answer is option C, $3x + 2$, and option A, $6x + 1 - 3x - 1$.

Final Answer

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Introduction

In our previous article, we explored the concept of simplifying algebraic expressions, focusing on the given expression $6x + 1 - (3x - 1)$. We simplified the expression and compared it with the given options. In this article, we will provide a Q&A guide to help you understand the concept of simplifying algebraic expressions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

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, follow these steps:

1. Evaluate the expression inside the parentheses.
2. Simplify the expression by combining like terms.

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable(s) raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Q: How do I combine like terms?

A: To combine like terms, follow these steps:

1. Identify the like terms in the expression.
2. Add or subtract the coefficients of the like terms.
3. Keep the variable(s) the same.

Q: What is the distributive property?

A: The distributive property is a rule that allows us to distribute a coefficient to multiple terms inside parentheses. The distributive property states that:

a(b + c) = ab + ac

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, follow these steps:

1. Identify the coefficient that needs to be distributed.
2. Multiply the coefficient by each term inside the parentheses.
3. Simplify the expression by combining like terms.

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

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

• Forgetting to evaluate expressions inside parentheses.
• Not combining like terms.
• Not using the distributive property when necessary.
• Making errors when multiplying or dividing coefficients.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By following the order of operations (PEMDAS), evaluating expressions inside parentheses, and combining like terms, you can simplify even the most complex expressions. Remember to use the distributive property when necessary and avoid common mistakes to ensure accurate results.

Final Tips

• Practice, practice, practice! The more you practice simplifying algebraic expressions, the more comfortable you will become with the process.
• Use online resources or math software to help you visualize and simplify expressions.
• Don't be afraid to ask for help if you are struggling with a particular concept or expression.

Common Algebraic Expressions

Here are some common algebraic expressions that you may encounter:

• $2x + 3$
• $x^2 + 4x + 4$
• $3x - 2$
• $x^2 - 4x + 4$
• $2x^2 + 3x - 1$

Simplifying Algebraic Expressions: A Summary

In this article, we provided a Q&A guide to help you understand the concept of simplifying algebraic expressions. We covered topics such as the order of operations (PEMDAS), simplifying expressions with parentheses, combining like terms, and using the distributive property. Remember to practice, practice, practice, and don't be afraid to ask for help if you are struggling with a particular concept or expression.