Simplify The Expression Shown:$\[3x + 2 - 3x + 7 + 5x\\]What Is The Coefficient In The Simplified Expression?A. 5 B. 9 C. 3 D. 5x

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: $3x + 2 - 3x + 7 + 5x$. We will break down the steps involved in simplifying this expression and identify the coefficient in the simplified expression.

Understanding Algebraic Expressions

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Variables are represented by letters, such as x, y, or z, while constants are numbers. Algebraic expressions can be combined using various mathematical operations, including addition, subtraction, multiplication, and division.

Simplifying the Given Expression

To simplify the given 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 perform multiplication and division operations from left to right.
4. Addition and Subtraction: We need to perform addition and subtraction operations from left to right.

Let's simplify the given expression step by step:

$3x + 2 - 3x + 7 + 5x$

Step 1: Combine like terms

We can combine the like terms, which are the terms that have the same variable. In this case, we have three terms with the variable x: $3x$, $-3x$, and $5x$. We can combine these terms as follows:

$3x - 3x + 5x$

Step 2: Simplify the expression

Now, we can simplify the expression by combining the like terms:

$3x - 3x + 5x = 5x$

Step 3: Add the constants

We have two constants in the expression: 2 and 7. We can add these constants as follows:

$2 + 7 = 9$

Step 4: Combine the simplified expression and the constant

Now, we can combine the simplified expression and the constant:

$5x + 9$

The Simplified Expression

The simplified expression is $5x + 9$. This is the final simplified form of the given expression.

Identifying the Coefficient

The coefficient of a term is the numerical value that is multiplied by the variable. In the simplified expression $5x + 9$, the coefficient of the term $5x$ is 5.

Conclusion

In this article, we simplified the given expression $3x + 2 - 3x + 7 + 5x$ by following the order of operations (PEMDAS). We combined like terms, simplified the expression, and added the constants. The simplified expression is $5x + 9$, and the coefficient of the term $5x$ is 5.

Final Answer

The final answer is $\boxed{5}$.

Discussion

What do you think is the most challenging part of simplifying algebraic expressions? Do you have any tips or tricks for simplifying expressions? Share your thoughts in the comments below!

Related Topics

• Simplifying expressions with exponents
• Combining like terms
• Order of operations (PEMDAS)
• Algebraic expressions

References

• Algebraic Expressions
• Order of Operations
• Simplifying Expressions
  Simplifying Algebraic Expressions: A Q&A Guide =====================================================

Introduction

In our previous article, we simplified the expression $3x + 2 - 3x + 7 + 5x$ and identified the coefficient in the simplified expression. In this article, we will answer some frequently asked questions (FAQs) about simplifying algebraic expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

• 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 an expression with exponents?

A: To simplify an expression with exponents, you need to follow the order of operations (PEMDAS). If the expression contains parentheses, evaluate the expression inside the parentheses first. Then, evaluate any exponential expressions next. Finally, evaluate any multiplication and division operations from left to right.

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, x is a variable. A constant is a number that does not change. For example, 5 is a constant.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable and coefficient. Then, add or subtract the coefficients of the like terms.

Q: What is the coefficient of a term?

A: The coefficient of a term is the numerical value that is multiplied by the variable. For example, in the term 3x, the coefficient is 3.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow the order of operations (PEMDAS). If the expression contains parentheses, evaluate the expression inside the parentheses first. Then, simplify any fractions by dividing the numerator and denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I simplify an expression with decimals?

A: To simplify an expression with decimals, you need to follow the order of operations (PEMDAS). If the expression contains parentheses, evaluate the expression inside the parentheses first. Then, simplify any decimals by performing the operations as usual.

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression that contains only one variable and has a degree of 1. For example, 2x + 3 is a linear expression. A quadratic expression is an expression that contains only one variable and has a degree of 2. For example, x^2 + 4x + 5 is a quadratic expression.

Q: How do I simplify an expression with absolute values?

A: To simplify an expression with absolute values, you need to follow the order of operations (PEMDAS). If the expression contains parentheses, evaluate the expression inside the parentheses first. Then, simplify any absolute values by removing the absolute value symbol and evaluating the expression inside.

Conclusion

In this article, we answered some frequently asked questions (FAQs) about simplifying algebraic expressions. We covered topics such as the order of operations (PEMDAS), combining like terms, and simplifying expressions with exponents, fractions, decimals, and absolute values.

Final Answer

The final answer is $\boxed{5}$.

Discussion

What do you think is the most challenging part of simplifying algebraic expressions? Do you have any tips or tricks for simplifying expressions? Share your thoughts in the comments below!

Related Topics

• Simplifying expressions with exponents
• Combining like terms
• Order of operations (PEMDAS)
• Algebraic expressions

References

• Algebraic Expressions
• Order of Operations
• Simplifying Expressions