Subtract:$(4x + 7) - (x + 1)$A. $4x + 8$B. $ 4 X + 6 4x + 6 4 X + 6 [/tex]C. $3x + 8$D. $3x + 6$

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Understanding the Problem

When dealing with algebraic expressions, subtraction involves removing or taking away one expression from another. In this case, we are given the expression $(4x + 7) - (x + 1)$, and we need to simplify it by subtracting the second expression from the first.

Step 1: Distribute the Negative Sign

To simplify the expression, we need to distribute the negative sign to the terms inside the second parentheses. This means that we will change the sign of each term inside the parentheses.

Step 2: Apply the Distributive Property

Using the distributive property, we can rewrite the expression as follows:

$(4x + 7) - (x + 1) = 4x + 7 - x - 1$

Step 3: Combine Like Terms

Now that we have distributed the negative sign, 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 $x$, and two constant terms.

Step 4: Simplify the Expression

Combining like terms, we get:

$4x + 7 - x - 1 = 3x + 6$

Conclusion

Therefore, the simplified expression is $3x + 6$. This is the correct answer.

Answer Choice Analysis

Let's analyze the answer choices to see why the other options are incorrect.

• Option A: $4x + 8$ is incorrect because it does not take into account the subtraction of the second expression.
• Option B: $4x + 6$ is incorrect because it does not correctly distribute the negative sign to the terms inside the second parentheses.
• Option D: $3x + 6$ is the correct answer, but it is not the only option. However, it is the only option that correctly simplifies the expression.

Final Answer

The final answer is $\boxed{3x + 6}$.

Why is this Important?

Understanding how to subtract algebraic expressions is an important skill in mathematics. It is used in a variety of applications, such as solving equations and inequalities, and working with functions. By mastering this skill, you will be able to solve a wide range of mathematical problems.

Real-World Applications

Subtracting algebraic expressions has many real-world applications. For example, it is used in finance to calculate the difference between two investments, and in science to calculate the difference between two measurements.

Common Mistakes

When subtracting algebraic expressions, there are several common mistakes to watch out for. These include:

• Failing to distribute the negative sign to the terms inside the second parentheses.
• Failing to combine like terms.
• Not taking into account the subtraction of the second expression.

Tips and Tricks

Here are some tips and tricks to help you master the skill of subtracting algebraic expressions:

• Make sure to distribute the negative sign to the terms inside the second parentheses.
• Combine like terms carefully.
• Take into account the subtraction of the second expression.

Practice Problems

Here are some practice problems to help you master the skill of subtracting algebraic expressions:

• $(3x + 2) - (2x + 1)$
• $(x + 4) - (x + 3)$
• $(2x + 5) - (x + 2)$

Conclusion

In conclusion, subtracting algebraic expressions is an important skill in mathematics. By mastering this skill, you will be able to solve a wide range of mathematical problems. Remember to distribute the negative sign to the terms inside the second parentheses, combine like terms carefully, and take into account the subtraction of the second expression. With practice and patience, you will become proficient in subtracting algebraic expressions.

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Frequently Asked Questions

Q: What is the first step in subtracting algebraic expressions?

A: The first step in subtracting algebraic expressions is to distribute the negative sign to the terms inside the second parentheses.

Q: Why is it important to distribute the negative sign?

A: Distributing the negative sign is important because it allows us to change the sign of each term inside the parentheses, which is necessary for subtracting the second expression from the first.

Q: What is the next step after distributing the negative sign?

A: After distributing the negative sign, the next step is to combine like terms. Like terms are terms that have the same variable raised to the same power.

Q: What is the final step in subtracting algebraic expressions?

A: The final step in subtracting algebraic expressions is to simplify the expression by combining like terms and removing any unnecessary parentheses.

Q: What are some common mistakes to watch out for when subtracting algebraic expressions?

A: Some common mistakes to watch out for when subtracting algebraic expressions include failing to distribute the negative sign, failing to combine like terms, and not taking into account the subtraction of the second expression.

Q: How can I practice subtracting algebraic expressions?

A: You can practice subtracting algebraic expressions by working through example problems, such as the ones listed below:

• $(3x + 2) - (2x + 1)$
• $(x + 4) - (x + 3)$
• $(2x + 5) - (x + 2)$

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

A: Subtracting algebraic expressions has many real-world applications, such as calculating the difference between two investments in finance, and calculating the difference between two measurements in science.

Q: Why is it important to master the skill of subtracting algebraic expressions?

A: Mastering the skill of subtracting algebraic expressions is important because it allows you to solve a wide range of mathematical problems, and is a fundamental skill in mathematics.

Q: What are some tips and tricks for mastering the skill of subtracting algebraic expressions?

A: Some tips and tricks for mastering the skill of subtracting algebraic expressions include:

• Make sure to distribute the negative sign to the terms inside the second parentheses.
• Combine like terms carefully.
• Take into account the subtraction of the second expression.

Additional Resources

If you are struggling with subtracting algebraic expressions, there are many additional resources available to help you. These include:

• Online tutorials and videos
• Practice problems and worksheets
• Math textbooks and study guides
• Online math communities and forums

Conclusion

In conclusion, subtracting algebraic expressions is an important skill in mathematics. By mastering this skill, you will be able to solve a wide range of mathematical problems. Remember to distribute the negative sign to the terms inside the second parentheses, combine like terms carefully, and take into account the subtraction of the second expression. With practice and patience, you will become proficient in subtracting algebraic expressions.

Final Tips

• Practice, practice, practice! The more you practice subtracting algebraic expressions, the more comfortable you will become with the skill.
• Don't be afraid to ask for help if you are struggling. There are many resources available to help you master the skill of subtracting algebraic expressions.
• Take your time and be careful when working through problems. Subtracting algebraic expressions requires attention to detail and careful calculation.

Related Topics

• Adding algebraic expressions
• Multiplying algebraic expressions
• Dividing algebraic expressions
• Solving linear equations and inequalities
• Working with functions and graphs

Glossary

• Algebraic expression: A mathematical expression that contains variables and constants.
• Like terms: Terms that have the same variable raised to the same power.
• Distributive property: A property of algebraic expressions that allows us to distribute a coefficient to each term inside a parentheses.
• Negative sign: A symbol that indicates the opposite of a value or expression.
• Parentheses: Symbols used to group terms or expressions together.