Which Expression Is Equivalent To $3m + 1 - M$?A. $2 + M - 1 + M$ B. $ 1 + M 1 + M 1 + M [/tex] C. $3m - 1$ D. $3m$

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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, with a focus on the given expression $3m + 1 - m$. We will examine each option and determine which one is equivalent to the given expression.

Understanding the Given Expression

The given expression is $3m + 1 - m$. To simplify this expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are $3m$ and $-m$.

Simplifying the Expression

To simplify the expression, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the like terms. In this case, we have:

3m+1−m3m + 1 - m

We can combine the like terms by adding the coefficients:

3m−m=2m3m - m = 2m

So, the simplified expression is $2m + 1$.

Evaluating the Options

Now that we have simplified the expression, we can evaluate the options. Let's examine each option and determine which one is equivalent to the simplified expression.

Option A: $2 + m - 1 + m$

This option is not equivalent to the simplified expression. The expression $2 + m - 1 + m$ can be simplified as follows:

2+m−1+m=1+2m2 + m - 1 + m = 1 + 2m

This is not equivalent to the simplified expression $2m + 1$.

Option B: $1 + m$

This option is not equivalent to the simplified expression. The expression $1 + m$ is a simplified form of the original expression, but it is not equivalent to the simplified expression $2m + 1$.

Option C: $3m - 1$

This option is not equivalent to the simplified expression. The expression $3m - 1$ is a simplified form of the original expression, but it is not equivalent to the simplified expression $2m + 1$.

Option D: $3m$

This option is not equivalent to the simplified expression. The expression $3m$ is a simplified form of the original expression, but it is not equivalent to the simplified expression $2m + 1$.

Conclusion

In conclusion, the simplified expression $2m + 1$ is not equivalent to any of the given options. However, we can see that the expression $3m - 1$ is close to the simplified expression, but it is missing the constant term $1$. Therefore, the correct answer is not among the given options.

What We Learned

In this article, we learned how to simplify algebraic expressions by combining like terms. We also learned how to evaluate options and determine which one is equivalent to the simplified expression. We saw that the simplified expression $2m + 1$ is not equivalent to any of the given options, but we can see that the expression $3m - 1$ is close to the simplified expression.

Tips and Tricks

Here are some tips and tricks for simplifying algebraic expressions:

  • Combine like terms by adding or subtracting the coefficients.
  • Simplify the expression by combining like terms.
  • Evaluate options and determine which one is equivalent to the simplified expression.
  • Use the distributive property to simplify expressions.

Practice Problems

Here are some practice problems to help you master the skill of simplifying algebraic expressions:

  1. Simplify the expression $2x + 3 - x$.
  2. Simplify the expression $4y - 2 + 2y$.
  3. Simplify the expression $6z + 1 - 2z$.

Answer Key

Here is the answer key for the practice problems:

  1. x+3x + 3

  2. 6y−26y - 2

  3. 4z+14z + 1

Conclusion

Introduction

In our previous article, we explored the process of simplifying algebraic expressions, with a focus on the given expression $3m + 1 - m$. We also learned some tips and tricks for simplifying algebraic expressions and practiced with some sample problems. In this article, we will continue to explore the topic of simplifying algebraic expressions by answering some frequently asked questions.

Q&A

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 $4x$ 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 expression with multiple like terms?

A: To simplify an expression with multiple like terms, you need to combine the like terms by adding or subtracting the coefficients. For example, if you have the expression $2x + 3x - 4x$, you can combine the like terms by adding the coefficients:

2x+3x−4x=(2+3−4)x=x2x + 3x - 4x = (2 + 3 - 4)x = x

Q: What is the distributive property, and how do I use it to simplify expressions?

A: The distributive property is a rule that states that you can multiply a single term to multiple terms inside parentheses. For example, if you have the expression $2(x + 3)$, you can use the distributive property to simplify it as follows:

2(x+3)=2x+62(x + 3) = 2x + 6

Q: How do I simplify an expression with a negative coefficient?

A: To simplify an expression with a negative coefficient, you need to change the sign of the coefficient and the term. For example, if you have the expression $-2x$, you can simplify it by changing the sign of the coefficient and the term:

−2x=−1(2x)=−2x-2x = -1(2x) = -2x

Q: What is the difference between a simplified expression and a factored expression?

A: A simplified expression is an expression that has been combined to its simplest form, with no like terms remaining. For example, the expression $2x + 3x$ is simplified to $5x$. A factored expression is an expression that has been written as a product of two or more terms. For example, the expression $5x$ can be factored as $5(x)$.

Tips and Tricks

Here are some additional tips and tricks for simplifying algebraic expressions:

  • Always combine like terms first.
  • Use the distributive property to simplify expressions with multiple terms inside parentheses.
  • Change the sign of the coefficient and the term when simplifying expressions with negative coefficients.
  • Simplify expressions by combining like terms and using the distributive property.

Practice Problems

Here are some additional practice problems to help you master the skill of simplifying algebraic expressions:

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

Answer Key

Here is the answer key for the practice problems:

  1. x−4x=−3xx - 4x = -3x

  2. 2x+62x + 6

  3. xx

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By combining like terms, using the distributive property, and simplifying expressions with negative coefficients, we can simplify complex expressions and make them easier to work with. We also learned some additional tips and tricks for simplifying algebraic expressions and practiced with some sample problems.