Simplify The Expression:\[$-9x - X + 3 + 5\$\]

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 the given expression: ${-9x - x + 3 + 5}$. 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 variables and constants. It consists of three terms: ${-9x}$, ${-x}$, and ${3 + 5}$. To simplify this expression, we need to combine like terms, which are terms that have the same variable raised to the same power.

Step 1: Identify Like Terms

The first step in simplifying the expression is to identify like terms. In this case, we have two terms that contain the variable ${x}$: ${-9x}$ and ${-x}$. These two terms are like terms because they both contain the variable ${x}$ raised to the power of 1.

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them. To combine like terms, we add or subtract their coefficients. In this case, we have:

${-9x - x = -10x}$

So, the expression now becomes:

${-10x + 3 + 5}$

Step 3: Simplify the Constants

The next step is to simplify the constants. In this case, we have two constants: ${3}$ and ${5}$. We can add these constants together to get:

${3 + 5 = 8}$

So, the expression now becomes:

${-10x + 8}$

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the steps outlined in this article, we can simplify the given expression: ${-9x - x + 3 + 5}$. We identified like terms, combined them, and simplified the constants to arrive at the final simplified expression: ${-10x + 8}$.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to identify like terms and combine them.
• When combining like terms, add or subtract their coefficients.
• Simplify the constants by adding or subtracting them.
• Always check your work by plugging in values for the variables to ensure that the expression is simplified correctly.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In economics, algebraic expressions are used to model economic systems. In computer science, algebraic expressions are used to write algorithms and programs.

Common Mistakes to Avoid

When simplifying algebraic expressions, there are several common mistakes to avoid. These include:

• Failing to identify like terms
• Failing to combine like terms
• Failing to simplify the constants
• Making arithmetic errors when combining like terms or simplifying the constants

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the steps outlined in this article, we can simplify the given expression: ${-9x - x + 3 + 5}$. We identified like terms, combined them, and simplified the constants to arrive at the final simplified expression: ${-10x + 8}$. Remember to always check your work by plugging in values for the variables to ensure that the expression is simplified correctly.

Final Answer

The final simplified expression is:

${-10x + 8}$

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions

References

• "Algebra and Trigonometry" by Michael Sullivan
• "Calculus" by Michael Spivak
• "Linear Algebra and Its Applications" by Gilbert Strang
  Simplifying Algebraic Expressions: A Q&A Guide =====================================================

Introduction

Simplifying algebraic expressions is a fundamental concept in mathematics, and it's essential to understand the process to solve equations and inequalities. In this article, we will provide a Q&A guide to help you understand the steps involved in simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a combination of variables, constants, and mathematical operations. It's a way to represent a mathematical relationship between variables and constants.

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 contain the variable ${x}$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients. For example, if you have ${2x + 5x}$, you can combine them by adding their coefficients: ${2x + 5x = 7x}$.

Q: What are the steps to simplify an algebraic expression?

A: The steps to simplify an algebraic expression are:

1. Identify like terms
2. Combine like terms
3. Simplify the constants

Q: How do I simplify the constants?

A: To simplify the constants, you add or subtract them. For example, if you have ${3 + 5}$, you can simplify them by adding them: ${3 + 5 = 8}$.

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 identify like terms
• Failing to combine like terms
• Failing to simplify the constants
• Making arithmetic errors when combining like terms or simplifying the constants

Q: How do I check my work when simplifying algebraic expressions?

A: To check your work when simplifying algebraic expressions, you can plug in values for the variables and see if the expression is simplified correctly. For example, if you have the expression ${2x + 5x}$, you can plug in ${x = 1}$ and see if the expression simplifies to ${7x}$.

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

A: Simplifying algebraic expressions has numerous real-world applications, including:

• Physics: Algebraic expressions are used to describe the motion of objects.
• Economics: Algebraic expressions are used to model economic systems.
• Computer Science: Algebraic expressions are used to write algorithms and programs.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working through examples and exercises. You can also use online resources, such as Khan Academy or Mathway, to practice simplifying algebraic expressions.

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the steps outlined in this article, you can simplify algebraic expressions and apply them to real-world problems. Remember to always check your work by plugging in values for the variables to ensure that the expression is simplified correctly.

Final Answer

The final simplified expression is:

${-10x + 8}$

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions

References

• "Algebra and Trigonometry" by Michael Sullivan
• "Calculus" by Michael Spivak
• "Linear Algebra and Its Applications" by Gilbert Strang