Substitute 3 For $x$ And Evaluate The Expression Below: $6x - 2$.A. 16 B. 6 C. 7 D. 12

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill to master. In this article, we will focus on substituting a value into an algebraic expression and evaluating it. We will use the expression $6x - 2$ as an example and substitute $x = 3$ to find the final value.

What is an Algebraic Expression?

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using symbols and mathematical notation. Algebraic expressions can be simple or complex, and they can be used to solve equations, inequalities, and other mathematical problems.

Substituting a Value into an Algebraic Expression

To substitute a value into an algebraic expression, we need to replace the variable with the given value. In this case, we are given the expression $6x - 2$ and we need to substitute $x = 3$ into it. To do this, we will replace the variable $x$ with the value $3$ and simplify the expression.

Evaluating the Expression

To evaluate the expression $6x - 2$, we need to follow the order of operations (PEMDAS):

  1. Parentheses: None
  2. Exponents: None
  3. Multiplication and Division: Multiply $6$ and $x$, and then subtract $2$.
  4. Addition and Subtraction: None

Now, let's substitute $x = 3$ into the expression:

6x−26x - 2

Replace $x$ with $3$:

6(3)−26(3) - 2

Multiply $6$ and $3$:

18−218 - 2

Subtract $2$ from $18$:

1616

Therefore, the final value of the expression $6x - 2$ when $x = 3$ is $16$.

Conclusion

Evaluating algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of the order of operations and how to substitute values into expressions. In this article, we used the expression $6x - 2$ as an example and substituted $x = 3$ to find the final value. We followed the order of operations (PEMDAS) and simplified the expression to arrive at the final answer.

Frequently Asked Questions

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.

Q: How do I substitute a value into an algebraic expression?

A: To substitute a value into an algebraic expression, you need to replace the variable with the given value and simplify the expression.

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

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

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to follow the order of operations (PEMDAS) and simplify the expression.

Example Problems

Problem 1

Evaluate the expression $2x + 5$ when $x = 4$.

Solution

Replace $x$ with $4$:

2(4)+52(4) + 5

Multiply $2$ and $4$:

8+58 + 5

Add $5$ to $8$:

1313

Therefore, the final value of the expression $2x + 5$ when $x = 4$ is $13$.

Problem 2

Evaluate the expression $x^2 - 3x + 2$ when $x = 2$.

Solution

Replace $x$ with $2$:

(2)2−3(2)+2(2)^2 - 3(2) + 2

Square $2$:

4−3(2)+24 - 3(2) + 2

Multiply $3$ and $2$:

4−6+24 - 6 + 2

Subtract $6$ from $4$:

−2+2-2 + 2

Add $2$ to $-2$:

00

Therefore, the final value of the expression $x^2 - 3x + 2$ when $x = 2$ is $0$.

Practice Problems

Problem 1

Evaluate the expression $3x - 2$ when $x = 5$.

Problem 2

Evaluate the expression $x^2 + 4x - 5$ when $x = 3$.

Problem 3

Evaluate the expression $2x^2 - 3x + 1$ when $x = 2$.

Problem 4

Evaluate the expression $x^2 - 2x - 3$ when $x = 4$.

Problem 5

Evaluate the expression $3x^2 + 2x - 1$ when $x = 3$.

Final Answer

The final answer is: 16\boxed{16}

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill to master. In this article, we will answer some of the most frequently asked questions about algebraic expressions, including how to substitute values, evaluate expressions, and more.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.

Q: How do I substitute a value into an algebraic expression?

A: To substitute a value into an algebraic expression, you need to replace the variable with the given value and simplify the expression.

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

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

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to follow the order of operations (PEMDAS) and simplify the expression.

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

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary operations.

Q: What is a like term?

A: A like term is a term that has the same variable and exponent as another term.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms.

Q: What is a coefficient?

A: A coefficient is a number that is multiplied by a variable.

Q: How do I eliminate unnecessary operations?

A: To eliminate unnecessary operations, you need to simplify the expression by combining like terms and eliminating any unnecessary parentheses or exponents.

Advanced Q&A

Q: What is a polynomial expression?

A: A polynomial expression is an algebraic expression that consists of variables and constants, and only contains addition, subtraction, and multiplication operations.

Q: How do I evaluate a polynomial expression?

A: To evaluate a polynomial expression, you need to follow the order of operations (PEMDAS) and simplify the expression.

Q: What is a rational expression?

A: A rational expression is an algebraic expression that consists of variables and constants, and contains division operations.

Q: How do I evaluate a rational expression?

A: To evaluate a rational expression, you need to follow the order of operations (PEMDAS) and simplify the expression.

Q: What is a radical expression?

A: A radical expression is an algebraic expression that contains a square root or other radical operation.

Q: How do I evaluate a radical expression?

A: To evaluate a radical expression, you need to follow the order of operations (PEMDAS) and simplify the expression.

Example Problems

Problem 1

Evaluate the expression $2x + 5$ when $x = 4$.

Solution

Replace $x$ with $4$:

2(4)+52(4) + 5

Multiply $2$ and $4$:

8+58 + 5

Add $5$ to $8$:

1313

Therefore, the final value of the expression $2x + 5$ when $x = 4$ is $13$.

Problem 2

Evaluate the expression $x^2 - 3x + 2$ when $x = 2$.

Solution

Replace $x$ with $2$:

(2)2−3(2)+2(2)^2 - 3(2) + 2

Square $2$:

4−3(2)+24 - 3(2) + 2

Multiply $3$ and $2$:

4−6+24 - 6 + 2

Subtract $6$ from $4$:

−2+2-2 + 2

Add $2$ to $-2$:

00

Therefore, the final value of the expression $x^2 - 3x + 2$ when $x = 2$ is $0$.

Practice Problems

Problem 1

Evaluate the expression $3x - 2$ when $x = 5$.

Problem 2

Evaluate the expression $x^2 + 4x - 5$ when $x = 3$.

Problem 3

Evaluate the expression $2x^2 - 3x + 1$ when $x = 2$.

Problem 4

Evaluate the expression $x^2 - 2x - 3$ when $x = 4$.

Problem 5

Evaluate the expression $3x^2 + 2x - 1$ when $x = 3$.

Final Answer

The final answer is: 16\boxed{16}