Select The Correct Expressions.Identify The Equivalent Expressions Of $4(2x + X - 3) - 3x + 3$.A. $9x - 9$B. \$9x - 1$[/tex\]C. $9x + X - 9$D. $9(x - 1)$E. $4(3x - 3) + 3 - 3x$

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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 $4(2x + x - 3) - 3x + 3$ and identify its equivalent expressions. We will break down the process into manageable steps, making it easier to understand and apply.

Step 1: Distribute the Coefficient

The first step in simplifying the expression is to distribute the coefficient 4 to the terms inside the parentheses.

4(2x+x−3)−3x+34(2x + x - 3) - 3x + 3

Using the distributive property, we multiply 4 to each term inside the parentheses:

8x+4x−12−3x+38x + 4x - 12 - 3x + 3

Step 2: Combine Like Terms

Now that we have distributed the coefficient, we can combine like terms. Like terms are terms that have the same variable raised to the same power.

8x+4x−12−3x+38x + 4x - 12 - 3x + 3

We can combine the like terms 8x8x, 4x4x, and −3x-3x:

9x−12+39x - 12 + 3

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression further by combining the constants.

9x−12+39x - 12 + 3

We can combine the constants −12-12 and 33:

9x−99x - 9

Conclusion

In conclusion, the simplified expression is $9x - 9$. This is the equivalent expression of the original expression $4(2x + x - 3) - 3x + 3$.

Comparison with the Options

Now that we have simplified the expression, we can compare it with the options provided:

A. $9x - 9$ B. $9x - 1$ C. $9x + x - 9$ D. $9(x - 1)$ E. $4(3x - 3) + 3 - 3x$

The correct answer is A. $9x - 9$.

Why is this the correct answer?

This is the correct answer because we have simplified the expression $4(2x + x - 3) - 3x + 3$ to $9x - 9$, which matches option A.

What about the other options?

Let's take a closer look at the other options:

B. $9x - 1$

This option is incorrect because the constant term is −1-1, not −9-9.

C. $9x + x - 9$

This option is incorrect because the expression is not simplified correctly.

D. $9(x - 1)$

This option is incorrect because the expression is not simplified correctly.

E. $4(3x - 3) + 3 - 3x$

This option is incorrect because the expression is not simplified correctly.

Conclusion

In conclusion, the correct answer is A. $9x - 9$. This is the equivalent expression of the original expression $4(2x + x - 3) - 3x + 3$. We have broken down the process into manageable steps, making it easier to understand and apply.

Final Thoughts

Introduction

In our previous article, we discussed how to simplify the expression $4(2x + x - 3) - 3x + 3$ and identify its equivalent expressions. In this article, we will provide a Q&A guide to help you understand and apply the concepts.

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to distribute the coefficient to the terms inside the parentheses.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to multiply a coefficient to each term inside the parentheses.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable raised to the same power. Then, you can add or subtract the coefficients of those terms.

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 different powers of the same variable.

Q: How do I simplify an expression with multiple terms?

A: To simplify an expression with multiple terms, you need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expressions inside the parentheses.
  2. Exponents: Evaluate any exponential expressions.
  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 is the final step in simplifying an algebraic expression?

A: The final step in simplifying an algebraic expression is to simplify the expression by combining any like terms.

Q: How do I identify equivalent expressions?

A: To identify equivalent expressions, you need to simplify the expression and then compare it to the original expression.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

  • Not distributing the coefficient to the terms inside the parentheses.
  • Not combining like terms.
  • Not following the order of operations (PEMDAS).
  • Not simplifying the expression by combining any like terms.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill to master in mathematics. By following the steps outlined in this article and avoiding common mistakes, you can simplify expressions and identify their equivalent expressions.

Final Thoughts

Simplifying algebraic expressions is a skill that takes practice to develop. With patience and persistence, you can become proficient in simplifying expressions and identifying their equivalent expressions.

Common Algebraic Expressions and Their Simplified Forms

Here are some common algebraic expressions and their simplified forms:

  • 2(3x + 2) - 5x + 3$ = $6x + 4 - 5x + 3$ = $x + 7

  • 4(2x - 3) + 2x - 1$ = $8x - 12 + 2x - 1$ = $10x - 13

  • 3(2x + 1) - 2x + 4$ = $6x + 3 - 2x + 4$ = $4x + 7

Practice Problems

Here are some practice problems to help you apply the concepts:

  • Simplify the expression $5(3x - 2) + 2x - 3$.
  • Simplify the expression $2(4x + 3) - 3x + 2$.
  • Simplify the expression $3(2x - 1) + 2x + 4$.

Answer Key

Here are the answers to the practice problems:

  • 5(3x - 2) + 2x - 3$ = $15x - 10 + 2x - 3$ = $17x - 13

  • 2(4x + 3) - 3x + 2$ = $8x + 6 - 3x + 2$ = $5x + 8

  • 3(2x - 1) + 2x + 4$ = $6x - 3 + 2x + 4$ = $8x + 1