Simplify $6-4[x+1-(y+3)]+5y$.A. $-4+2x+3y$ B. $8+2x+3y$ C. $14-4x+9y$ D. $22-4x+9y$
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression, $6-4[x+1-(y+3)]+5y$, and explore the various steps involved in the process.
Understanding the Expression
Before we dive into the simplification process, let's take a closer look at the given expression:
This expression consists of several components, including:
- A constant term: 6
- A variable term: x
- A nested expression:
- Another variable term: 5y
Step 1: Distributing the Negative Sign
The first step in simplifying the expression is to distribute the negative sign to the terms inside the brackets:
Step 2: Combining Like Terms
Now that we have distributed the negative sign, we can combine like terms:
Step 3: Simplifying the Constants
Next, we can simplify the constants by combining them:
Step 4: Final Simplification
Finally, we can simplify the expression by combining the constants:
Conclusion
In conclusion, simplifying the algebraic expression $6-4[x+1-(y+3)]+5y$ involves several steps, including distributing the negative sign, combining like terms, simplifying the constants, and final simplification. By following these steps, we can arrive at the simplified expression: $14-4x+9y$.
Answer
The correct answer is:
C.
Discussion
This problem requires a deep understanding of algebraic expressions and the ability to simplify them using various techniques. The key to solving this problem is to carefully distribute the negative sign, combine like terms, and simplify the constants. By following these steps, we can arrive at the correct solution.
Tips and Tricks
Here are some tips and tricks to help you simplify algebraic expressions:
- Always distribute the negative sign to the terms inside the brackets.
- Combine like terms by adding or subtracting the coefficients of the variables.
- Simplify the constants by combining them.
- Use the order of operations (PEMDAS) to ensure that you are simplifying the expression correctly.
Practice Problems
Here are some practice problems to help you improve your skills in simplifying algebraic expressions:
- Simplify the expression: $2x+3y-4[x+1-(y+3)]+5y$
- Simplify the expression: $6-4[x+1-(y+3)]+5y+2x$
- Simplify the expression: $2x+3y-4[x+1-(y+3)]+5y-2x$
Conclusion
Introduction
In our previous article, we explored the process of simplifying algebraic expressions, focusing on the expression $6-4[x+1-(y+3)]+5y$. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.
Q&A
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 sign to the terms inside the brackets.
Q: How do I combine like terms in an algebraic expression?
A: To combine like terms, add or subtract the coefficients of the variables. For example, if you have the expression $2x+3x$, you can combine the like terms by adding the coefficients: $2x+3x = 5x$.
Q: What is the order of operations (PEMDAS) and how does it apply to simplifying algebraic expressions?
A: The order of operations (PEMDAS) is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
When simplifying algebraic expressions, it's essential to follow the order of operations to ensure that you are simplifying the expression correctly.
Q: How do I simplify an algebraic expression with multiple variables?
A: To simplify an algebraic expression with multiple variables, follow the same steps as before:
- Distribute the negative sign to the terms inside the brackets.
- Combine like terms by adding or subtracting the coefficients of the variables.
- Simplify the constants by combining them.
- Use the order of operations (PEMDAS) to ensure that you are simplifying the expression correctly.
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 the negative sign to the terms inside the brackets.
- Not combining like terms correctly.
- Not simplifying the constants correctly.
- Not following the order of operations (PEMDAS).
Q: How can I practice simplifying algebraic expressions?
A: There are many resources available to help you practice simplifying algebraic expressions, including:
- Online practice problems and quizzes.
- Algebra textbooks and workbooks.
- Online algebra courses and tutorials.
- Practice problems in this article.
Conclusion
Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the steps outlined in this article and practicing regularly, you can improve your skills and become more confident in your ability to simplify complex expressions. Remember to always distribute the negative sign, combine like terms, simplify the constants, and use the order of operations (PEMDAS) to ensure that you are simplifying the expression correctly.
Additional Resources
Practice Problems
Here are some practice problems to help you improve your skills in simplifying algebraic expressions:
- Simplify the expression: $2x+3y-4[x+1-(y+3)]+5y$
- Simplify the expression: $6-4[x+1-(y+3)]+5y+2x$
- Simplify the expression: $2x+3y-4[x+1-(y+3)]+5y-2x$