What Is The Simplified Expression For The Expression Below? { -1(2x + 3) - 2(x - 1)$}$A. { -4x + 1$}$ B. { -4x - 2$}$ C. { -4x + 2$}$ D. { -4x - 1$}$

What is the Simplified Expression for the Given Algebraic Expression?

Understanding the Problem

The given algebraic expression is ${-1(2x + 3) - 2(x - 1)}$. We are asked to simplify this expression and choose the correct answer from the options provided.

Step 1: Distribute the Negative Signs

To simplify the expression, we need to start by distributing the negative signs inside the parentheses. When we multiply a negative number by a positive number, the result is always negative. Therefore, we can rewrite the expression as:

${-1(2x + 3) = -2x - 3}$ ${-2(x - 1) = -2x + 2}$

Step 2: Combine Like Terms

Now that we have distributed the negative signs, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable x:

${-2x - 3 - 2x + 2}$

We can combine the two terms with x by adding their coefficients:

${-2x - 2x = -4x}$

So, the expression becomes:

${-4x - 3 + 2}$

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by combining the constants:

${-3 + 2 = -1}$

Therefore, the simplified expression is:

${-4x - 1}$

Conclusion

The simplified expression for the given algebraic expression is ${-4x - 1}$. This is the correct answer.

Answer Choice

The correct answer is:

• D. ${-4x - 1}$

Why is this the Correct Answer?

This is the correct answer because we simplified the expression by distributing the negative signs and combining like terms. We also simplified the constants by combining them. The final expression is ${-4x - 1}$, which matches the correct answer.

What is the Importance of Simplifying Algebraic Expressions?

Simplifying algebraic expressions is an important skill in mathematics because it helps us to:

• Understand the structure of the expression: By simplifying the expression, we can see the underlying structure and relationships between the terms.
• Perform calculations more easily: Simplified expressions are often easier to work with and can make calculations more straightforward.
• Identify patterns and relationships: Simplified expressions can help us to identify patterns and relationships between the terms, which can be useful in solving problems.

Common Mistakes to Avoid

When simplifying algebraic expressions, there are several common mistakes to avoid:

• Not distributing negative signs: Failing to distribute negative signs can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
• Not simplifying constants: Failing to simplify constants can lead to incorrect simplifications.

Tips for Simplifying Algebraic Expressions

Here are some tips for simplifying algebraic expressions:

• Distribute negative signs carefully: Make sure to distribute negative signs correctly to avoid incorrect simplifications.
• Combine like terms carefully: Make sure to combine like terms correctly to avoid incorrect simplifications.
• Simplify constants carefully: Make sure to simplify constants correctly to avoid incorrect simplifications.
• Check your work: Always check your work to ensure that the simplified expression is correct.

Conclusion

Simplifying algebraic expressions is an important skill in mathematics that helps us to understand the structure of the expression, perform calculations more easily, and identify patterns and relationships. By following the steps outlined in this article and avoiding common mistakes, we can simplify algebraic expressions with confidence.
Frequently Asked Questions (FAQs) about Simplifying Algebraic Expressions

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to distribute the negative signs inside the parentheses. This involves multiplying the negative sign by each term inside the parentheses.

Q: How do I distribute negative signs correctly?

A: To distribute negative signs correctly, you need to multiply the negative sign by each term inside the parentheses. For example, if you have the expression ${-1(2x + 3)}$, you would multiply the negative sign by each term inside the parentheses to get ${-2x - 3}$.

Q: What is the next step in simplifying an algebraic expression?

A: The next step in simplifying an algebraic expression is 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 their coefficients.

Q: How do I combine like terms correctly?

A: To combine like terms correctly, you need to add the coefficients of the like terms. For example, if you have the expression ${-2x - 2x}$, you would add the coefficients to get ${-4x}$.

Q: What is the final step in simplifying an algebraic expression?

A: The final step in simplifying an algebraic expression is to simplify the constants. This involves combining any constants that are added or subtracted.

Q: How do I simplify constants correctly?

A: To simplify constants correctly, you need to combine any constants that are added or subtracted. For example, if you have the expression ${-3 + 2}$, you would combine the constants to get ${-1}$.

Q: Why is it important to simplify algebraic expressions?

A: Simplifying algebraic expressions is important because it helps us to:

• Understand the structure of the expression: By simplifying the expression, we can see the underlying structure and relationships between the terms.
• Perform calculations more easily: Simplified expressions are often easier to work with and can make calculations more straightforward.
• Identify patterns and relationships: Simplified expressions can help us to identify patterns and relationships between the terms, which can be useful in solving problems.

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

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

• Not distributing negative signs: Failing to distribute negative signs can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
• Not simplifying constants: Failing to simplify constants can lead to incorrect simplifications.

Q: How can I check my work when simplifying algebraic expressions?

A: To check your work when simplifying algebraic expressions, you can:

• Re-read the expression: Make sure you understand the expression and the steps you need to take to simplify it.
• Check your calculations: Make sure you have performed the calculations correctly and that the simplified expression is correct.
• Use a calculator or computer: If you are unsure about the simplified expression, you can use a calculator or computer to check your work.

Q: What are some tips for simplifying algebraic expressions?

A: Some tips for simplifying algebraic expressions include:

• Distribute negative signs carefully: Make sure to distribute negative signs correctly to avoid incorrect simplifications.
• Combine like terms carefully: Make sure to combine like terms correctly to avoid incorrect simplifications.
• Simplify constants carefully: Make sure to simplify constants correctly to avoid incorrect simplifications.
• Check your work: Always check your work to ensure that the simplified expression is correct.

Conclusion

Simplifying algebraic expressions is an important skill in mathematics that helps us to understand the structure of the expression, perform calculations more easily, and identify patterns and relationships. By following the steps outlined in this article and avoiding common mistakes, we can simplify algebraic expressions with confidence.