Evaluate The Expression − 2 ( 2 X + Z ) − Y -2(2x + Z) - Y − 2 ( 2 X + Z ) − Y When X = − 1 X = -1 X = − 1 , Y = 2 Y = 2 Y = 2 , And Z = − 3 Z = -3 Z = − 3 .

Mar 12, 2025 by ADMIN 158 views

Evaluate the Expression: A Step-by-Step Guide

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Introduction

In algebra, evaluating expressions is a crucial skill that helps us solve problems and make sense of mathematical equations. In this article, we will evaluate the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ . We will break down the expression into smaller parts, substitute the given values, and simplify the expression to find the final result.

Understanding the Expression

The given expression is $-2(2x + z) - y$ . This expression involves variables $x$ , $y$ , and $z$ , as well as arithmetic operations such as multiplication and addition. To evaluate this expression, we need to follow the order of operations (PEMDAS):

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Substituting the Given Values

We are given the values of $x$ , $y$ , and $z$ as $x = -1$ , $y = 2$ , and $z = -3$ . We will substitute these values into the expression $-2(2x + z) - y$ .

x = -1
y = 2
z = -3
expression = -2 * (2 * x + z) - y

Evaluating the Expression

Now that we have substituted the given values, we can evaluate the expression step by step.

Step 1: Evaluate the expression inside the parentheses

The expression inside the parentheses is $2x + z$ . We will substitute the value of $x$ and $z$ into this expression.

expression_inside_parentheses = 2 * x + z

Step 2: Multiply $-2$ by the expression inside the parentheses

Now that we have evaluated the expression inside the parentheses, we will multiply $-2$ by this expression.

result = -2 * expression_inside_parentheses

Step 3: Subtract $y$ from the result

Finally, we will subtract $y$ from the result.

final_result = result - y

Calculating the Final Result

Now that we have broken down the expression into smaller parts, we can calculate the final result.

x = -1
y = 2
z = -3
expression_inside_parentheses = 2 * x + z
result = -2 * expression_inside_parentheses
final_result = result - y
print(final_result)

Conclusion

In this article, we evaluated the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ . We broke down the expression into smaller parts, substituted the given values, and simplified the expression to find the final result. The final result is $\boxed{-12}$ .

Frequently Asked Questions

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 we have multiple operations in an expression. The acronym PEMDAS stands for:

Parentheses
Exponents
Multiplication and Division
Addition and Subtraction

Q: How do I evaluate an expression with variables?

A: To evaluate an expression with variables, we need to substitute the given values of the variables into the expression and then simplify the expression.

Q: What is the final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ ?

A: The final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ is $\boxed{-12}$ .

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Introduction

In our previous article, we evaluated the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ . We broke down the expression into smaller parts, substituted the given values, and simplified the expression to find the final result. In this article, we will answer some frequently asked questions about evaluating 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 we have multiple operations in an expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate 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 evaluate an expression with variables?

A: To evaluate an expression with variables, you need to substitute the given values of the variables into the expression and then simplify the expression. For example, if you have the expression $2x + 3$ and you know that $x = 4$ , you would substitute $x = 4$ into the expression to get $2(4) + 3 = 8 + 3 = 11$ .

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

A: An expression is a group of numbers, variables, and mathematical operations that are combined using mathematical symbols. An equation, on the other hand, is a statement that says two expressions are equal. For example, $2x + 3 = 5$ is an equation, while $2x + 3$ is an expression.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and eliminate any unnecessary operations. For example, if you have the expression $2x + 3 + 2x$ , you can combine the like terms to get $4x + 3$ .

Q: What is the final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ ?

A: The final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ is $\boxed{-12}$ .

Q: How do I evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, you need to substitute the given values of all the variables into the expression and then simplify the expression. For example, if you have the expression $2x + 3y - z$ and you know that $x = 4$ , $y = 2$ , and $z = 3$ , you would substitute these values into the expression to get $2(4) + 3(2) - 3 = 8 + 6 - 3 = 11$ .

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

A: A variable is a symbol that represents a value that can change. A constant, on the other hand, is a value that does not change. For example, $x$ is a variable, while $3$ is a constant.

Conclusion

In this article, we answered some frequently asked questions about evaluating expressions. We covered topics such as the order of operations, evaluating expressions with variables, simplifying expressions, and more. We hope that this article has been helpful in clarifying any confusion you may have had about evaluating expressions.

Frequently Asked Questions

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 we have multiple operations in an expression. The acronym PEMDAS stands for:

Parentheses
Exponents
Multiplication and Division
Addition and Subtraction

Q: How do I evaluate an expression with variables?

A: To evaluate an expression with variables, you need to substitute the given values of the variables into the expression and then simplify the expression.

Q: What is the final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ ?

A: The final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ is $\boxed{-12}$ .

Q: How do I simplify an expression?

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

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

A: An expression is a group of numbers, variables, and mathematical operations that are combined using mathematical symbols. An equation, on the other hand, is a statement that says two expressions are equal.

Additional Resources

We hope that this article has been helpful in clarifying any confusion you may have had about evaluating expressions. If you have any further questions, please don't hesitate to ask.

Introduction

Understanding the Expression

Substituting the Given Values

Evaluating the Expression

Step 1: Evaluate the expression inside the parentheses

Step 2: Multiply −2-2−2 by the expression inside the parentheses

Step 3: Subtract yyy from the result

Calculating the Final Result

Conclusion

Frequently Asked Questions

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

Q: How do I evaluate an expression with variables?

Q: What is the final result of the expression −2(2x+z)−y-2(2x + z) - y−2(2x+z)−y when x=−1x = -1x=−1, y=2y = 2y=2, and z=−3z = -3z=−3?

Introduction

Q&A

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

Q: How do I evaluate an expression with variables?

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

Q: How do I simplify an expression?

Q: What is the final result of the expression −2(2x+z)−y-2(2x + z) - y−2(2x+z)−y when x=−1x = -1x=−1, y=2y = 2y=2, and z=−3z = -3z=−3?

Q: How do I evaluate an expression with multiple variables?

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

Conclusion

Frequently Asked Questions

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

Q: How do I evaluate an expression with variables?

Q: What is the final result of the expression −2(2x+z)−y-2(2x + z) - y−2(2x+z)−y when x=−1x = -1x=−1, y=2y = 2y=2, and z=−3z = -3z=−3?

Q: How do I simplify an expression?

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

Additional Resources

Step 2: Multiply $-2$ by the expression inside the parentheses

Step 3: Subtract $y$ from the result

Q: What is the final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ ?

Q: What is the final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ ?

Q: What is the final result of the expression $-2(2x + z) - y$ when $x = -1$ , $y = 2$ , and $z = -3$ ?