Simplify 4 ( X + 7 ) − 7 X + 2 4(x+7)-7x+2 4 ( X + 7 ) − 7 X + 2 .A. 11 X + 9 11x+9 11 X + 9 B. 11 X + 30 11x+30 11 X + 30 C. − 3 X + 30 -3x+30 − 3 X + 30 D. − 3 X + 9 -3x+9 − 3 X + 9

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Understanding the Problem

In this problem, we are given an algebraic expression $4(x+7)-7x+2$ and we need to simplify it. Simplifying an algebraic expression means combining like terms and performing any necessary operations to reduce the expression to its simplest form.

Step 1: Distribute the 4

To simplify the expression, we need to start by distributing the 4 to the terms inside the parentheses. This means multiplying the 4 by each term inside the parentheses.

4(x+7) = 4x + 28

Step 2: Rewrite the Expression

Now that we have distributed the 4, we can rewrite the expression as follows:

4x + 28 - 7x + 2

Step 3: Combine Like Terms

Next, we need to 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: 4x and -7x. We can combine these terms by adding their coefficients.

(4x - 7x) + 28 + 2

Step 4: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by performing any necessary operations. In this case, we can simplify the expression by combining the constants 28 and 2.

-3x + 30

Conclusion

In conclusion, the simplified form of the expression $4(x+7)-7x+2$ is $-3x + 30$.

Answer

The correct answer is C. $-3x+30$.

Why is this Important?

Simplifying algebraic expressions is an important skill in mathematics because it allows us to work with complex expressions in a more manageable way. By simplifying expressions, we can make it easier to solve equations and inequalities, and to understand the relationships between variables.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example, in physics, we often need to simplify complex expressions to understand the behavior of physical systems. In engineering, we may need to simplify expressions to design and optimize systems. In economics, we may need to simplify expressions to understand the relationships between economic variables.

Tips and Tricks

Here are some tips and tricks for simplifying algebraic expressions:

• Always start by distributing any coefficients to the terms inside the parentheses.
• Combine like terms by adding their coefficients.
• Simplify the expression by performing any necessary operations.
• Check your work by plugging in values for the variables and checking that the expression simplifies to the expected value.

Common Mistakes

Here are some common mistakes to avoid when simplifying algebraic expressions:

• Failing to distribute coefficients to terms inside parentheses.
• Failing to combine like terms.
• Failing to simplify the expression by performing necessary operations.
• Making errors when combining like terms or simplifying the expression.

Conclusion

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Q: What is the first step in simplifying the expression $4(x+7)-7x+2$?

A: The first step in simplifying the expression $4(x+7)-7x+2$ is to distribute the 4 to the terms inside the parentheses. This means multiplying the 4 by each term inside the parentheses.

Q: How do I distribute the 4 to the terms inside the parentheses?

A: To distribute the 4 to the terms inside the parentheses, you need to multiply the 4 by each term inside the parentheses. In this case, you would multiply the 4 by the x and the 7.

Q: What is the result of distributing the 4 to the terms inside the parentheses?

A: The result of distributing the 4 to the terms inside the parentheses is $4x + 28$.

Q: What is the next step in simplifying the expression $4(x+7)-7x+2$?

A: The next step in simplifying the expression $4(x+7)-7x+2$ is to rewrite the expression with the distributed 4.

Q: How do I rewrite the expression with the distributed 4?

A: To rewrite the expression with the distributed 4, you need to replace the $4(x+7)$ with $4x + 28$. The expression would then become $4x + 28 - 7x + 2$.

Q: What is the next step in simplifying the expression $4x + 28 - 7x + 2$?

A: The next step in simplifying the expression $4x + 28 - 7x + 2$ is to combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In this case, the like terms are the $4x$ and the $-7x$.

Q: How do I combine like terms?

A: To combine like terms, you need to add their coefficients. In this case, you would add the 4 and the -7 to get -3.

Q: What is the result of combining like terms?

A: The result of combining like terms is $-3x + 30$.

Q: What is the final step in simplifying the expression $4(x+7)-7x+2$?

A: The final step in simplifying the expression $4(x+7)-7x+2$ is to simplify the expression by performing any necessary operations.

Q: What is the final simplified form of the expression $4(x+7)-7x+2$?

A: The final simplified form of the expression $4(x+7)-7x+2$ is $-3x + 30$.

Q: Why is it important to simplify algebraic expressions?

A: Simplifying algebraic expressions is important because it allows us to work with complex expressions in a more manageable way. By simplifying expressions, we can make it easier to solve equations and inequalities, and to understand the relationships between variables.

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

A: Some real-world applications of simplifying algebraic expressions include physics, engineering, and economics. In these fields, we often need to simplify complex expressions to understand the behavior of physical systems, design and optimize systems, and understand the relationships between economic variables.

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

A: Some common mistakes to avoid when simplifying algebraic expressions include failing to distribute coefficients to terms inside parentheses, failing to combine like terms, and failing to simplify the expression by performing necessary operations.