Simplify And Write In Standard Form: $\[ 12x - 8x + 9 - 10 \\]

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of simplifying algebraic expressions, focusing on the given expression: ${ 12x - 8x + 9 - 10 }$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the underlying concepts.

Understanding Algebraic Expressions

An algebraic expression is a mathematical statement that combines variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants. Algebraic expressions can be simple or complex, and they can be used to solve equations, inequalities, and other mathematical problems.

Simplifying the Given Expression

The given expression is: ${ 12x - 8x + 9 - 10 }$. To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: There are no parentheses in the given expression.
  2. Exponents: There are no exponents in the given expression.
  3. Multiplication and Division: We need to evaluate the multiplication and division operations.
  4. Addition and Subtraction: We need to evaluate the addition and subtraction operations.

Step 1: Combine Like Terms

The given expression contains two like terms: 12x12x and −8x-8x. Like terms are terms that have the same variable and exponent. To combine like terms, we need to add or subtract their coefficients.

12x−8x=(12−8)x=4x{ 12x - 8x = (12 - 8)x = 4x }

So, the expression becomes: ${ 4x + 9 - 10 }$

Step 2: Simplify the Constants

The expression contains two constants: 99 and −10-10. We can simplify the constants by adding or subtracting them.

9−10=−1{ 9 - 10 = -1 }

So, the expression becomes: ${ 4x - 1 }$

Step 3: Final Simplification

The expression is now simplified, and we have: ${ 4x - 1 }$. This is the final simplified form of the given expression.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the order of operations and combining like terms, we can simplify complex expressions and make them easier to work with. In this article, we simplified the given expression: $ 12x - 8x + 9 - 10 }$, and we arrived at the final simplified form ${ 4x - 1 $. We hope this article has provided a clear understanding of the process of simplifying algebraic expressions.

Common Algebraic Expressions and Their Simplifications

Here are some common algebraic expressions and their simplifications:

  • 2x+3x=(2+3)x=5x{ 2x + 3x = (2 + 3)x = 5x }

  • 4x−2x=(4−2)x=2x{ 4x - 2x = (4 - 2)x = 2x }

  • 3x+2x=(3+2)x=5x{ 3x + 2x = (3 + 2)x = 5x }

  • 2x−3x=(2−3)x=−x{ 2x - 3x = (2 - 3)x = -x }

Tips and Tricks for Simplifying Algebraic Expressions

Here are some tips and tricks for simplifying algebraic expressions:

  • Combine like terms: Combine like terms by adding or subtracting their coefficients.
  • Simplify constants: Simplify constants by adding or subtracting them.
  • Follow the order of operations: Follow the order of operations (PEMDAS) to simplify expressions.
  • Use parentheses: Use parentheses to group terms and simplify expressions.

Practice Problems

Here are some practice problems to help you simplify algebraic expressions:

  • Simplify the expression: ${ 3x + 2x - 4x + 5 }$
  • Simplify the expression: ${ 2x - 3x + 4x - 2 }$
  • Simplify the expression: ${ 4x + 3x - 2x + 1 }$
  • Simplify the expression: ${ 2x - 4x + 3x - 1 }$

Conclusion

Introduction

In our previous article, we explored the process of simplifying algebraic expressions, focusing on the given expression: ${ 12x - 8x + 9 - 10 }$. We broke down the steps involved in simplifying this expression and provided a clear understanding of the underlying concepts. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x2x and 4x4x are like terms because they both have the variable xx and the same exponent (1).

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, if you have the expression 2x+4x2x + 4x, you can combine the like terms by adding their coefficients: 2x+4x=(2+4)x=6x2x + 4x = (2 + 4)x = 6x.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. For example, xx is a variable. A constant is a value that does not change. For example, 55 is a constant.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to evaluate the expression inside the parentheses first. For example, if you have the expression (2x+3)x(2x + 3)x, you need to evaluate the expression inside the parentheses first: (2x+3)x=2x2+3x(2x + 3)x = 2x^2 + 3x.

Q: What is the final simplified form of an expression?

A: The final simplified form of an expression is the simplest form of the expression, where all like terms have been combined and the expression has been evaluated according to the order of operations.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying algebraic expressions:

  • Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
  • Not combining like terms: Make sure to combine like terms by adding or subtracting their coefficients.
  • Not simplifying constants: Make sure to simplify constants by adding or subtracting them.
  • Not using parentheses: Make sure to use parentheses to group terms and simplify expressions.

Tips and Tricks

Here are some tips and tricks for simplifying algebraic expressions:

  • Use a calculator: Use a calculator to check your work and make sure you have simplified the expression correctly.
  • Check your work: Make sure to check your work by plugging in values for the variables and evaluating the expression.
  • Use a diagram: Use a diagram to visualize the expression and make sure you have simplified it correctly.
  • Practice, practice, practice: Practice simplifying expressions to become more comfortable with the process.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the order of operations and combining like terms, we can simplify complex expressions and make them easier to work with. We hope this article has provided a clear understanding of the process of simplifying algebraic expressions and has given you the confidence to tackle more complex expressions.