What Is $(2x + 3) + (7x - 1)$?A. $9x + 4$ B. \$9x + 2$[/tex\] C. $-5x + 4$ D. $-5x + 2$
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying the expression $(2x + 3) + (7x - 1)$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the process.
Understanding the Expression
The given expression is a combination of two algebraic expressions: $(2x + 3)$ and $(7x - 1)$. To simplify this expression, we need to combine like terms, which means combining the terms with the same variable.
Step 1: Distribute the Negative Sign
The first step in simplifying the expression is to distribute the negative sign to the terms inside the second parentheses. This will change the sign of each term inside the parentheses.
Step 2: 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: $2x$ and $-7x$. We can combine these terms by adding their coefficients.
Step 3: Simplify the Expression
Now that we have combined like terms, we can simplify the expression by evaluating the terms inside the parentheses.
Step 4: Write the Final Answer
The final step is to write the simplified expression in the correct format. In this case, we can write the expression as $-5x + 4$.
Conclusion
Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of the steps involved. By following the steps outlined in this article, we can simplify the expression $(2x + 3) + (7x - 1)$ and arrive at the final answer: $-5x + 4$.
Answer Key
The correct answer is:
- C. $-5x + 4$
Tips and Tricks
- When simplifying algebraic expressions, always start by distributing the negative sign to the terms inside the parentheses.
- Combine like terms by adding their coefficients.
- Simplify the expression by evaluating the terms inside the parentheses.
- Write the final answer in the correct format.
Common Mistakes
- Failing to distribute the negative sign to the terms inside the parentheses.
- Not combining like terms.
- Not simplifying the expression by evaluating the terms inside the parentheses.
Real-World Applications
Simplifying algebraic expressions has numerous real-world applications, including:
- Science and Engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
- Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.
- Computer Science: Algebraic expressions are used to write algorithms and solve problems in computer science.
Conclusion
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 parentheses.
Q: How do I combine like terms in an algebraic expression?
A: To combine like terms, you need to add the coefficients of the terms with the same variable. For example, if you have the expression $(2x + 3) + (7x - 1)$, you can combine the like terms by adding the coefficients of the x terms: $2x + 7x = 9x$.
Q: What is the difference between a like term and a unlike term?
A: A like term is a term that has the same variable raised to the same power. For example, $2x$ and $7x$ are like terms because they both have the variable x raised to the power of 1. A unlike term is a term that has a different variable or a different power of the variable. For example, $2x$ and $3y$ are unlike terms because they have different variables.
Q: How do I simplify an algebraic expression with multiple parentheses?
A: To simplify an algebraic expression with multiple parentheses, you need to follow the order of operations (PEMDAS):
- Evaluate the expressions inside the parentheses.
- Simplify the expression by combining like terms.
- Write the final answer in the correct format.
Q: What is the final answer to the expression $(2x + 3) + (7x - 1)$?
A: The final answer to the expression $(2x + 3) + (7x - 1)$ is $-5x + 4$.
Q: Can I simplify an algebraic expression with variables on both sides of the equation?
A: Yes, you can simplify an algebraic expression with variables on both sides of the equation. However, you need to follow the order of operations and combine like terms carefully.
Q: How do I check my work when simplifying an algebraic expression?
A: To check your work when simplifying an algebraic expression, you can:
- Plug in a value for the variable and evaluate the expression.
- Simplify the expression using a different method, such as factoring or using a calculator.
- Compare your answer to the original expression to ensure that it is correct.
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 parentheses.
- Not combining like terms.
- Not simplifying the expression by evaluating the terms inside the parentheses.
- Writing the final answer in the incorrect format.
Q: How can I practice simplifying algebraic expressions?
A: You can practice simplifying algebraic expressions by:
- Working through practice problems in a textbook or online resource.
- Creating your own practice problems and simplifying them.
- Using a calculator or online tool to check your work and get feedback.
- Joining a study group or working with a tutor to get help and support.
Conclusion
Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of the steps involved. By following the steps outlined in this article and practicing regularly, you can become proficient in simplifying algebraic expressions and apply this skill to a wide range of real-world problems.