Simplify The Expression: \[$-4 + 4x - 10x + 11\$\]A. \[$14x + 15\$\]B. \[$-6x + 7\$\]C. \[$14x + 7\$\]D. \[$15x - 14\$\]

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 simplifying a specific algebraic expression, which involves combining like terms and rearranging the expression to its simplest form. We will use the given expression ${-4 + 4x - 10x + 11}$ as an example and guide you through the step-by-step process of simplifying it.

Understanding Like Terms

Before we dive into simplifying the expression, it's essential to understand what like terms are. Like terms are terms that have the same variable raised to the same power. In other words, they are terms that have the same algebraic structure. For example, ${4x}$ and ${-10x}$ are like terms because they both have the variable ${x}$ raised to the power of 1.

Step 1: Identify Like Terms

The first step in simplifying the expression is to identify the like terms. In the given expression ${-4 + 4x - 10x + 11}$, we can see that there are two like terms: ${4x}$ and ${-10x}$. These two terms have the same variable ${x}$ raised to the power of 1.

Step 2: Combine Like Terms

Once we have identified the like terms, we can combine them by adding or subtracting their coefficients. In this case, we can combine the two like terms ${4x}$ and ${-10x}$ by adding their coefficients: ${4x - 10x = -6x}$. So, the expression now becomes ${-4 + (-6x) + 11}$.

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression further by rearranging the terms. We can start by combining the constant terms: ${-4 + 11 = 7}$. So, the expression now becomes ${7 - 6x}$.

Step 4: Write the Final Answer

The final step is to write the simplified expression in the correct format. In this case, the simplified expression is ${-6x + 7}$.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a step-by-step approach. By identifying like terms, combining them, and rearranging the expression, we can simplify complex expressions and arrive at their simplest form. In this article, we have used the expression ${-4 + 4x - 10x + 11}$ as an example and guided you through the step-by-step process of simplifying it.

Answer Key

The correct answer is ${B. \[-6x + 7}$].

Additional Examples

Here are a few additional examples of simplifying algebraic expressions:

• ${2x + 3x - 4x + 5}$ simplifies to ${0x + 5}$ or simply ${5}$.
• ${-3x + 2x + 4x - 1}$ simplifies to ${3x - 1}$.
• ${x + 2x - 3x + 4}$ simplifies to ${0x + 4}$ or simply ${4}$.

Tips and Tricks

Here are a few tips and tricks to help you simplify algebraic expressions:

• Always identify like terms first.
• Combine like terms by adding or subtracting their coefficients.
• Rearrange the expression to put the like terms together.
• Simplify the expression by combining constant terms.

By following these tips and tricks, you can simplify complex algebraic expressions and arrive at their simplest form.

Common Mistakes

Here are a few common mistakes to avoid when simplifying algebraic expressions:

• Not identifying like terms.
• Not combining like terms correctly.
• Not rearranging the expression to put the like terms together.
• Not simplifying the expression by combining constant terms.

By avoiding these common mistakes, you can simplify algebraic expressions accurately and efficiently.

Conclusion

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Introduction

In our previous article, we discussed the step-by-step process of simplifying algebraic expressions. We used the expression ${-4 + 4x - 10x + 11}$ as an example and guided you through the process of identifying like terms, combining them, and rearranging the expression. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In other words, they are terms that have the same algebraic structure. For example, ${4x}$ and ${-10x}$ are like terms because they both have the variable ${x}$ raised to the power of 1.

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable raised to the same power. You can do this by comparing the coefficients of the terms. If the coefficients are the same, then the terms are like terms.

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 two like terms ${4x}$ and ${-10x}$, you can combine them by adding their coefficients: ${4x - 10x = -6x}$.

Q: What is the order of operations when simplifying algebraic expressions?

A: The order of operations when simplifying algebraic expressions is:

1. Identify like terms.
2. Combine like terms by adding or subtracting their coefficients.
3. Rearrange the expression to put the like terms together.
4. Simplify the expression by combining constant terms.

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

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

• Not identifying like terms.
• Not combining like terms correctly.
• Not rearranging the expression to put the like terms together.
• Not simplifying the expression by combining constant terms.

Q: How do I simplify expressions with variables in the denominator?

A: To simplify expressions with variables in the denominator, you need to follow the same steps as before: identify like terms, combine them, and rearrange the expression. However, you also need to be careful when simplifying expressions with variables in the denominator, as you may need to multiply both the numerator and the denominator by the same value to eliminate the variable in the denominator.

Q: Can I simplify expressions with negative coefficients?

A: Yes, you can simplify expressions with negative coefficients. When simplifying expressions with negative coefficients, you need to remember that a negative coefficient is equivalent to a positive coefficient with a negative sign. For example, ${-4x}$ is equivalent to ${4(-x)}$.

Q: How do I simplify expressions with parentheses?

A: To simplify expressions with parentheses, you need to follow the order of operations: evaluate the expression inside the parentheses first, and then simplify the expression outside the parentheses.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a step-by-step approach. By identifying like terms, combining them, and rearranging the expression, we can simplify complex expressions and arrive at their simplest form. In this article, we have answered some frequently asked questions about simplifying algebraic expressions, including how to identify like terms, combine them, and avoid common mistakes.

Additional Resources

Here are some additional resources to help you simplify algebraic expressions:

• Khan Academy: Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions

By following these resources and practicing simplifying algebraic expressions, you can become proficient in this skill and apply it to a wide range of mathematical problems.

Practice Problems

Here are some practice problems to help you simplify algebraic expressions:

• Simplify the expression: ${2x + 3x - 4x + 5}$
• Simplify the expression: ${-3x + 2x + 4x - 1}$
• Simplify the expression: ${x + 2x - 3x + 4}$

By practicing simplifying algebraic expressions, you can develop your skills and become more confident in your ability to simplify complex expressions.