Evaluate The Expression When { A = 2$}$ And { B = 4$} . . . {4a - 2(a + B) + 1 = [?]\}

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Introduction

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In this article, we will evaluate the given expression when $a = 2$ and $b = 4$. The expression is $4a - 2(a + b) + 1$. We will follow a step-by-step approach to simplify the expression and find its value.

Understanding the Expression

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The given expression is $4a - 2(a + b) + 1$. To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expressions inside the parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Step 1: Evaluate the Expression Inside the Parentheses

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The expression inside the parentheses is $(a + b)$. We are given that $a = 2$ and $b = 4$. Therefore, we can substitute these values into the expression:

$(a + b) = (2 + 4) = 6$

Step 2: Substitute the Value of $(a + b)$ into the Expression

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Now that we have evaluated the expression inside the parentheses, we can substitute its value into the original expression:

$4a - 2(a + b) + 1 = 4a - 2(6) + 1$

Step 3: Simplify the Expression

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We can simplify the expression by evaluating the multiplication operation:

$4a - 2(6) + 1 = 4a - 12 + 1$

Step 4: Combine Like Terms

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We can combine the like terms in the expression:

$4a - 12 + 1 = 4a - 11$

Step 5: Substitute the Value of $a$ into the Expression

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We are given that $a = 2$. Therefore, we can substitute this value into the expression:

$4a - 11 = 4(2) - 11$

Step 6: Simplify the Expression

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We can simplify the expression by evaluating the multiplication operation:

$4(2) - 11 = 8 - 11$

Step 7: Evaluate the Final Expression

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We can evaluate the final expression by subtracting 11 from 8:

$8 - 11 = -3$

Conclusion

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In this article, we evaluated the given expression when $a = 2$ and $b = 4$. We followed a step-by-step approach to simplify the expression and find its value. The final value of the expression is $-3$.

Frequently Asked Questions

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• What is the value of the expression when $a = 2$ and $b = 4$?
  • The value of the expression is $-3$.
• How do I evaluate the expression when $a = 2$ and $b = 4$?
  • To evaluate the expression, follow the order of operations (PEMDAS) and substitute the values of $a$ and $b$ into the expression.

Final Answer

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The final answer is $\boxed{-3}$.

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Introduction

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In our previous article, we evaluated the expression $4a - 2(a + b) + 1$ when $a = 2$ and $b = 4$. We followed a step-by-step approach to simplify the expression and find its value. In this article, we will answer some frequently asked questions related to evaluating expressions.

Q&A

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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:

1. Parentheses: Evaluate the expressions inside the parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

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

A: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate the expressions inside the parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction 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. A constant is a value that does not change. In the expression $4a - 2(a + b) + 1$, $a$ and $b$ are variables, while $4$, $2$, and $1$ are constants.

Q: How do I simplify an expression with like terms?

A: To simplify an expression with like terms, combine the like terms by adding or subtracting their coefficients. For example, in the expression $4a - 2a + 1$, we can combine the like terms by adding the coefficients of $a$:

$4a - 2a + 1 = (4 - 2)a + 1 = 2a + 1$

Q: What is the value of the expression $2x + 3y - 4x + 2y$?

A: To evaluate the expression $2x + 3y - 4x + 2y$, we need to combine the like terms. We can do this by adding or subtracting the coefficients of $x$ and $y$:

$2x + 3y - 4x + 2y = (2 - 4)x + (3 + 2)y = -2x + 5y$

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, follow the order of operations (PEMDAS). First, evaluate the expressions inside the parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

For example, in the expression $\frac{2}{3}x + \frac{1}{2}y - \frac{3}{4}x + \frac{1}{2}y$, we can evaluate the expression by following the order of operations:

$\frac{2}{3}x + \frac{1}{2}y - \frac{3}{4}x + \frac{1}{2}y = \frac{2}{3}x - \frac{3}{4}x + \frac{1}{2}y + \frac{1}{2}y$

Next, we can combine the like terms by adding or subtracting the coefficients of $x$ and $y$:

$\frac{2}{3}x - \frac{3}{4}x + \frac{1}{2}y + \frac{1}{2}y = \left(\frac{2}{3} - \frac{3}{4}\right)x + \left(\frac{1}{2} + \frac{1}{2}\right)y = \left(\frac{8}{12} - \frac{9}{12}\right)x + \left(\frac{2}{2}\right)y = -\frac{1}{12}x + 1y$

Q: What is the value of the expression $\frac{1}{2}x + \frac{1}{3}y - \frac{1}{4}x + \frac{1}{2}y$?

A: To evaluate the expression $\frac{1}{2}x + \frac{1}{3}y - \frac{1}{4}x + \frac{1}{2}y$, we need to combine the like terms. We can do this by adding or subtracting the coefficients of $x$ and $y$:

$\frac{1}{2}x + \frac{1}{3}y - \frac{1}{4}x + \frac{1}{2}y = \left(\frac{1}{2} - \frac{1}{4}\right)x + \left(\frac{1}{3} + \frac{1}{2}\right)y = \left(\frac{2}{4} - \frac{1}{4}\right)x + \left(\frac{2}{6} + \frac{3}{6}\right)y = \frac{1}{4}x + \frac{5}{6}y$

Conclusion

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In this article, we answered some frequently asked questions related to evaluating expressions. We covered topics such as the order of operations (PEMDAS), simplifying expressions with like terms, and evaluating expressions with fractions. We hope that this article has been helpful in clarifying any confusion you may have had about evaluating expressions.

Final Answer

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The final answer is $\boxed{-3}$.