Select The Best Answer For The Question.What Is The Simplified Form Of $x - 1 + 4 + 7x - 3$?A. $8x$ B. $ 6 X + 3 6x + 3 6 X + 3 [/tex] C. $8x + 6$ D. $6x$
=====================================================
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 a specific algebraic expression, step by step, to arrive at the correct answer. We will use the given expression $x - 1 + 4 + 7x - 3$ as an example and explore the different options available.
Understanding the Expression
Before we begin simplifying the expression, let's take a closer look at it. The expression consists of four terms:
Combining Like Terms
The first step in simplifying the expression is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: $x$ and $7x$.
To combine these terms, we add their coefficients. The coefficient of $x$ is 1, and the coefficient of $7x$ is 7. Adding these coefficients, we get:
Simplifying the Constant Terms
Now that we have combined the like terms, let's focus on the constant terms. The constant terms are the terms that do not have a variable. In this case, we have two constant terms: $-1$ and $4$.
To simplify the constant terms, we add them together:
Combining the Simplified Terms
Now that we have simplified the like terms and the constant terms, let's combine them. We have two simplified terms: $8x$ and $3$.
To combine these terms, we add them together:
Evaluating the Options
Now that we have simplified the expression, let's evaluate the options available. We have four options:
A. $8x$ B. $6x + 3$ C. $8x + 6$ D. $6x$
Conclusion
Based on our step-by-step simplification of the expression, we can conclude that the correct answer is:
This is the simplified form of the given expression $x - 1 + 4 + 7x - 3$.
Final Answer
The final answer is:
Why is this the correct answer?
This is the correct answer because we have simplified the expression step by step, combining like terms and simplifying constant terms. We have also evaluated the options available and concluded that the correct answer is $8x + 3$.
What is the importance of simplifying algebraic expressions?
Simplifying algebraic expressions is an important skill in mathematics because it allows us to:
- Combine like terms and simplify constant terms
- Evaluate expressions and arrive at a correct answer
- Solve equations and inequalities
- Understand and apply mathematical concepts
What are some common mistakes to avoid when simplifying algebraic expressions?
Some common mistakes to avoid when simplifying algebraic expressions include:
- Failing to combine like terms
- Simplifying constant terms incorrectly
- Not evaluating the options available
- Not following the order of operations
What are some real-world applications of simplifying algebraic expressions?
Simplifying algebraic expressions has many real-world applications, including:
- Solving equations and inequalities in physics and engineering
- Modeling population growth and decay in biology
- Analyzing data and making predictions in statistics
- Solving optimization problems in economics
Conclusion
In conclusion, simplifying algebraic expressions is an important skill in mathematics that requires attention to detail and a step-by-step approach. By combining like terms and simplifying constant terms, we can arrive at a correct answer and evaluate the options available. With practice and patience, anyone can master the art of simplifying algebraic expressions and apply it to real-world problems.
=====================================================
Introduction
In our previous article, we explored the concept of simplifying algebraic expressions and provided a step-by-step guide on how to simplify a specific expression. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.
Q&A
Q: What is the difference between like terms and unlike terms?
A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers.
Q: How do I combine like terms?
A: To combine like terms, you add their coefficients. For example, if you have two like terms: $x$ and $7x$, you add their coefficients: $1 + 7 = 8$, resulting in $8x$.
Q: What is the order of operations when simplifying algebraic expressions?
A: The order of operations is:
- 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.
Q: How do I simplify constant terms?
A: To simplify constant terms, you add or subtract them as needed. For example, if you have two constant terms: $-1$ and $4$, you add them together: $-1 + 4 = 3$.
Q: What is the importance of simplifying algebraic expressions?
A: Simplifying algebraic expressions is an important skill in mathematics because it allows you to:
- Combine like terms and simplify constant terms
- Evaluate expressions and arrive at a correct answer
- Solve equations and inequalities
- Understand and apply mathematical concepts
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 combine like terms
- Simplifying constant terms incorrectly
- Not evaluating the options available
- Not following the order of operations
Q: How do I apply simplifying algebraic expressions to real-world problems?
A: Simplifying algebraic expressions has many real-world applications, including:
- Solving equations and inequalities in physics and engineering
- Modeling population growth and decay in biology
- Analyzing data and making predictions in statistics
- Solving optimization problems in economics
Conclusion
In conclusion, simplifying algebraic expressions is an important skill in mathematics that requires attention to detail and a step-by-step approach. By combining like terms and simplifying constant terms, we can arrive at a correct answer and evaluate the options available. With practice and patience, anyone can master the art of simplifying algebraic expressions and apply it to real-world problems.
Additional Resources
For further learning and practice, we recommend the following resources:
- Khan Academy: Algebra
- Mathway: Algebra Calculator
- Wolfram Alpha: Algebra Solver
Final Thoughts
Simplifying algebraic expressions is a fundamental concept in mathematics that has many real-world applications. By mastering this skill, you can solve equations and inequalities, model population growth and decay, analyze data and make predictions, and solve optimization problems. With practice and patience, you can become proficient in simplifying algebraic expressions and apply it to real-world problems.