Evaluate The Expression 3 X − 4 Y 3x - 4y 3 X − 4 Y When X = − 2 X = -2 X = − 2 And Y = 3 Y = 3 Y = 3 .Choose The Correct Answer:A. 18 B. 6 C. -18 D. -6

Mar 8, 2025 by ADMIN 156 views

Evaluate the Expression $3x - 4y$ When $x = -2$ and $y = 3$

Introduction

In algebra, evaluating an expression involves substituting given values for the variables in the expression and then simplifying the resulting expression. In this article, we will evaluate the expression $3x - 4y$ when $x = -2$ and $y = 3$ . We will use the given values to substitute into the expression and then simplify to find the final result.

Substituting Values into the Expression

To evaluate the expression $3x - 4y$ , we need to substitute the given values for $x$ and $y$ into the expression. The given values are $x = -2$ and $y = 3$ . We will substitute these values into the expression as follows:

$3x - 4y = 3(-2) - 4(3)$

Simplifying the Expression

Now that we have substituted the values into the expression, we can simplify the expression by following the order of operations (PEMDAS):

Multiply 3 and -2: $3(-2) = -6$
Multiply 4 and 3: $4(3) = 12$
Subtract 12 from -6: $-6 - 12 = -18$

Final Result

Therefore, the final result of evaluating the expression $3x - 4y$ when $x = -2$ and $y = 3$ is:

$3x - 4y = -18$

Conclusion

In this article, we evaluated the expression $3x - 4y$ when $x = -2$ and $y = 3$ . We substituted the given values into the expression and then simplified the resulting expression to find the final result. The final result is $-18$ , which is option C.

Frequently Asked Questions

What is the value of $3x - 4y$ when $x = -2$ and $y = 3$ ?
How do you evaluate an expression in algebra?
What is the order of operations (PEMDAS)?

Answer Key

The value of $3x - 4y$ when $x = -2$ and $y = 3$ is $-18$ .
To evaluate an expression in algebra, you need to substitute the given values into the expression and then simplify the resulting expression.
The order of operations (PEMDAS) is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Step-by-Step Solution

Substitute the given values into the expression: $3x - 4y = 3(-2) - 4(3)$
Simplify the expression by following the order of operations (PEMDAS):
- Multiply 3 and -2: $3(-2) = -6$
- Multiply 4 and 3: $4(3) = 12$
- Subtract 12 from -6: $-6 - 12 = -18$
The final result is $-18$ .

Example Problems

Evaluate the expression $2x + 5y$ when $x = 4$ and $y = 2$ .
Evaluate the expression $x^2 - 3y^2$ when $x = 3$ and $y = 2$ .
Evaluate the expression $4x - 2y$ when $x = -1$ and $y = 3$ .

Solution to Example Problems

Evaluate the expression $2x + 5y$ $2 x + 5 y$ when $x = 4$ $x = 4$ and $y = 2$ $y = 2$ :
- Substitute the given values into the expression: $2x + 5y = 2(4) + 5(2)$
- Simplify the expression by following the order of operations (PEMDAS):
  - Multiply 2 and 4: $2(4) = 8$
  - Multiply 5 and 2: $5(2) = 10$
  - Add 8 and 10: $8 + 10 = 18$
- The final result is $18$ .
Evaluate the expression $x^2 - 3y^2$ $x^{2} - 3 y^{2}$ when $x = 3$ $x = 3$ and $y = 2$ $y = 2$ :
- Substitute the given values into the expression: $x^2 - 3y^2 = (3)^2 - 3(2)^2$
- Simplify the expression by following the order of operations (PEMDAS):
  - Square 3: $(3)^2 = 9$
  - Square 2: $(2)^2 = 4$
  - Multiply 3 and 4: $3(4) = 12$
  - Subtract 12 from 9: $9 - 12 = -3$
- The final result is $-3$ .
Evaluate the expression $4x - 2y$ $4 x - 2 y$ when $x = -1$ $x = - 1$ and $y = 3$ $y = 3$ :
- Substitute the given values into the expression: $4x - 2y = 4(-1) - 2(3)$
- Simplify the expression by following the order of operations (PEMDAS):
  - Multiply 4 and -1: $4(-1) = -4$
  - Multiply 2 and 3: $2(3) = 6$
  - Subtract 6 from -4: $-4 - 6 = -10$
- The final result is $-10$ .

Introduction

Evaluating expressions in algebra is an essential skill that is used in a wide range of mathematical and real-world applications. In this article, we will answer some frequently asked questions about evaluating expressions in algebra.

Q: What is an expression in algebra?

A: An expression in algebra is a combination of variables, constants, and mathematical operations that can be simplified to a single value.

Q: How do I evaluate an expression in algebra?

A: To evaluate an expression in algebra, you need to substitute the given values into the expression and then simplify the resulting expression by following the order of operations (PEMDAS).

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 simplifying an expression. The order of operations is:

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 substitute values into an expression?

A: To substitute values into an expression, you need to replace the variables in the expression with the given values. For example, if the expression is $2x + 5y$ and the values are $x = 4$ and $y = 2$ , you would substitute the values into the expression as follows:

$2x + 5y = 2(4) + 5(2)$

Q: What is the difference between an expression and an equation?

A: An expression is a combination of variables, constants, and mathematical operations that can be simplified to a single value. An equation is a statement that says two expressions are equal. For example, the expression $2x + 5y$ is a combination of variables and constants, while the equation $2x + 5y = 10$ is a statement that says the expression $2x + 5y$ is equal to 10.

Q: How do I simplify an expression?

A: To simplify an expression, you need to follow the order of operations (PEMDAS) and combine like terms. Like terms are terms that have the same variable raised to the same power. For example, the expression $2x + 3x$ can be simplified by combining the like terms as follows:

$2x + 3x = 5x$

Q: What is the final result of evaluating an expression?

A: The final result of evaluating an expression is the simplified value of the expression. For example, if the expression is $2x + 5y$ and the values are $x = 4$ and $y = 2$ , the final result would be:

$2x + 5y = 2(4) + 5(2) = 8 + 10 = 18$

Q: How do I use expressions in real-world applications?

A: Expressions are used in a wide range of real-world applications, including science, engineering, economics, and finance. For example, expressions can be used to model population growth, predict stock prices, or calculate the cost of a product.

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

A: Some common mistakes to avoid when evaluating expressions include:

Not following the order of operations (PEMDAS)
Not combining like terms
Not substituting values into the expression correctly
Not simplifying the expression correctly

Q: How can I practice evaluating expressions?

A: You can practice evaluating expressions by working through examples and exercises in a textbook or online resource. You can also try creating your own expressions and evaluating them to see if you can simplify them correctly.

Q: What are some resources for learning more about evaluating expressions?

A: Some resources for learning more about evaluating expressions include:

Textbooks and online resources that cover algebra and mathematical operations
Online tutorials and videos that explain how to evaluate expressions
Practice exercises and worksheets that allow you to practice evaluating expressions
Online communities and forums where you can ask questions and get help from others.