Combine The Terms And Find The Coefficient Of $x$ In The Expression $3x + 8 + 5x$.A. 8 B. 4 C. 1 D. 7
Introduction
In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable raised to the same power. In this article, we will focus on combining like terms and finding the coefficient of a variable in a given expression. We will use the expression $3x + 8 + 5x$ as an example to demonstrate the process.
Understanding Like Terms
Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. On the other hand, $2x$ and $3y$ are not like terms because they have different variables.
Combining Like Terms
To combine like terms, we need to add or subtract the coefficients of the terms. The coefficient of a term is the number that is multiplied by the variable. For example, in the term $3x$, the coefficient is 3.
Let's combine the like terms in the expression $3x + 8 + 5x$. We can start by identifying the like terms, which are $3x$ and $5x$. We can then add their coefficients to get the combined coefficient.
Finding the Coefficient of x
To find the coefficient of $x$ in the expression $3x + 8 + 5x$, we need to combine the like terms and then identify the coefficient of $x$ in the resulting expression.
We can combine the like terms by adding their coefficients:
So, the expression becomes:
Now, we can identify the coefficient of $x$, which is 8.
Conclusion
In this article, we learned how to combine like terms and find the coefficient of a variable in a given expression. We used the expression $3x + 8 + 5x$ as an example to demonstrate the process. By combining like terms and identifying the coefficient of $x$, we can simplify complex expressions and make them easier to work with.
Answer
The correct answer is A. 8.
Additional Examples
Here are a few more examples of combining like terms and finding the coefficient of a variable:
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The coefficient of $x$ is 5.
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The coefficient of $x$ is 6.
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The coefficient of $x$ is 5.
Tips and Tricks
Here are a few tips and tricks to help you combine like terms and find the coefficient of a variable:
- Make sure to identify the like terms in the expression.
- Add or subtract the coefficients of the like terms.
- Identify the coefficient of the variable in the resulting expression.
- Simplify the expression by combining like terms.
Introduction
In our previous article, we discussed how to combine like terms and find the coefficient of a variable in a given expression. In this article, we will provide a Q&A section to help you better understand the concept and apply it to different scenarios.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract the coefficients of the terms. The coefficient of a term is the number that is multiplied by the variable. For example, in the term $3x$, the coefficient is 3.
Q: What is the coefficient of a variable?
A: The coefficient of a variable is the number that is multiplied by the variable. For example, in the term $3x$, the coefficient is 3.
Q: How do I find the coefficient of x in an expression?
A: To find the coefficient of $x$ in an expression, you need to combine the like terms and then identify the coefficient of $x$ in the resulting expression.
Q: What if I have an expression with multiple variables?
A: If you have an expression with multiple variables, you need to identify the like terms for each variable and then combine them separately.
Q: Can I combine like terms with different variables?
A: No, you cannot combine like terms with different variables. For example, you cannot combine $2x$ and $3y$ because they have different variables.
Q: What if I have an expression with a negative coefficient?
A: If you have an expression with a negative coefficient, you need to remember that a negative sign is attached to the coefficient, not the variable.
Q: How do I simplify an expression with like terms?
A: To simplify an expression with like terms, you need to combine the like terms and then simplify the resulting expression.
Q: Can I use a calculator to find the coefficient of a variable?
A: Yes, you can use a calculator to find the coefficient of a variable. However, it's always a good idea to understand the concept and apply it manually to ensure accuracy.
Q: What are some common mistakes to avoid when combining like terms?
A: Some common mistakes to avoid when combining like terms include:
- Not identifying the like terms in the expression.
- Not adding or subtracting the coefficients of the like terms.
- Not identifying the coefficient of the variable in the resulting expression.
- Not simplifying the expression after combining like terms.
Conclusion
In this Q&A article, we provided answers to common questions about combining like terms and finding the coefficient of a variable. We hope this article helps you better understand the concept and apply it to different scenarios.
Additional Resources
Here are some additional resources to help you learn more about combining like terms and finding the coefficient of a variable:
- Khan Academy: Combining Like Terms
- Mathway: Combining Like Terms
- IXL: Combining Like Terms
By following these resources and practicing the concept, you can become more confident in your ability to combine like terms and find the coefficient of a variable.