Simplify: 3 ( 2 Y + 4 ) − 8 3(2y + 4) - 8 3 ( 2 Y + 4 ) − 8 A. 5 Y + 14 5y + 14 5 Y + 14 B. 6 Y − 4 6y - 4 6 Y − 4 C. 6 Y + 4 6y + 4 6 Y + 4 D. 6 Y + 12 6y + 12 6 Y + 12

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Understanding the Problem

In this problem, we are given an algebraic expression that needs to be simplified. The expression is $3(2y + 4) - 8$. Our goal is to simplify this expression by combining like terms and performing any necessary operations.

Step 1: Distribute the 3

To simplify the expression, we need to start by distributing the 3 to the terms inside the parentheses. This means that we multiply the 3 by each term inside the parentheses.

3(2y + 4) = 3(2y) + 3(4)

Step 2: Simplify the Terms

Now that we have distributed the 3, we can simplify the terms inside the parentheses.

3(2y) = 6y
3(4) = 12

So, the expression becomes:

6y + 12 - 8

Step 3: Combine Like Terms

Now that we have simplified the terms, we can combine like terms. In this case, we have a constant term (-8) that we can combine with the constant term (12).

6y + 12 - 8 = 6y + 4

The Final Answer

Therefore, the simplified expression is $6y + 4$.

Conclusion

In this problem, we simplified the algebraic expression $3(2y + 4) - 8$ by distributing the 3, simplifying the terms, and combining like terms. The final answer is $6y + 4$.

Key Takeaways

• Distributing the 3 to the terms inside the parentheses is the first step in simplifying the expression.
• Simplifying the terms inside the parentheses is the next step in simplifying the expression.
• Combining like terms is the final step in simplifying the expression.

Common Mistakes

• Failing to distribute the 3 to the terms inside the parentheses.
• Failing to simplify the terms inside the parentheses.
• Failing to combine like terms.

Real-World Applications

Simplifying algebraic expressions is an important skill in mathematics that has many real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Practice Problems

1. Simplify the expression $2(3x + 2) - 5$.
2. Simplify the expression $4(2y - 3) + 2$.
3. Simplify the expression $3(2x + 1) - 2$.

Answer Key

1. $6x + 4 - 5 = 6x - 1$
2. $8y - 12 + 2 = 8y - 10$
3. $6x + 3 - 2 = 6x + 1$
   Simplify: $3(2y + 4) - 8$ - Q&A =====================================

Q: What is the first step in simplifying the expression $3(2y + 4) - 8$?

A: The first step in simplifying the expression $3(2y + 4) - 8$ is to distribute the 3 to the terms inside the parentheses.

Q: How do I distribute the 3 to the terms inside the parentheses?

A: To distribute the 3 to the terms inside the parentheses, you multiply the 3 by each term inside the parentheses. In this case, you would multiply the 3 by the 2y and the 4.

Q: What is the result of distributing the 3 to the terms inside the parentheses?

A: The result of distributing the 3 to the terms inside the parentheses is:

3(2y + 4) = 3(2y) + 3(4)

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

A: The next step in simplifying the expression is to simplify the terms inside the parentheses.

Q: How do I simplify the terms inside the parentheses?

A: To simplify the terms inside the parentheses, you multiply the 3 by each term inside the parentheses. In this case, you would multiply the 3 by the 2y and the 4.

Q: What is the result of simplifying the terms inside the parentheses?

A: The result of simplifying the terms inside the parentheses is:

3(2y) = 6y
3(4) = 12

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

A: The next step in simplifying the expression is to combine like terms.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract the coefficients of the like terms. In this case, you would add the 12 and the -8.

Q: What is the result of combining like terms?

A: The result of combining like terms is:

6y + 12 - 8 = 6y + 4

Q: What is the final answer to the expression $3(2y + 4) - 8$?

A: The final answer to the expression $3(2y + 4) - 8$ is $6y + 4$.

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

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

• Failing to distribute the 3 to the terms inside the parentheses.
• Failing to simplify the terms inside the parentheses.
• Failing to combine like terms.

Q: How do I practice simplifying expressions?

A: You can practice simplifying expressions by working through practice problems, such as:

1. Simplify the expression $2(3x + 2) - 5$.
2. Simplify the expression $4(2y - 3) + 2$.
3. Simplify the expression $3(2x + 1) - 2$.

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

A: Some real-world applications of simplifying expressions include:

• Physics: Algebraic expressions are used to describe the motion of objects.
• Engineering: Algebraic expressions are used to design and optimize systems.
• Economics: Algebraic expressions are used to model and analyze economic systems.

Q: How do I know if I have simplified an expression correctly?

A: You can check if you have simplified an expression correctly by:

• Checking your work to make sure you distributed the 3 correctly.
• Checking your work to make sure you simplified the terms correctly.
• Checking your work to make sure you combined like terms correctly.

Q: What if I get stuck on a problem?

A: If you get stuck on a problem, you can try:

• Breaking the problem down into smaller steps.
• Asking a teacher or tutor for help.
• Working through practice problems to build your skills.