Evaluate The Expression $-b + 8x$ When $b = 4$ And $x = -7$.

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Introduction

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In algebra, evaluating expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will evaluate the expression $-b + 8x$ when $b = 4$ and $x = -7$. We will break down the problem step by step, using simple language and clear explanations.

Understanding the Expression

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The given expression is $-b + 8x$. To evaluate this expression, we need to substitute the values of $b$ and $x$ into the expression. The expression consists of two terms: $-b$ and $8x$. The negative sign in front of $b$ indicates that we need to multiply $b$ by $-1$.

Substituting Values

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We are given that $b = 4$ and $x = -7$. To substitute these values into the expression, we will replace $b$ with $4$ and $x$ with $-7$.

Evaluating the Expression

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Now that we have substituted the values, we can evaluate the expression. We will start by evaluating the term $-b$. Since $b = 4$, we have:

$-b = -4$

Next, we will evaluate the term $8x$. Since $x = -7$, we have:

$8x = 8(-7) = -56$

Now that we have evaluated both terms, we can combine them to get the final result.

Combining Terms

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To combine the terms, we will add $-4$ and $-56$. When we add two negative numbers, we get a negative result. Therefore, we have:

$-b + 8x = -4 + (-56) = -60$

Conclusion

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In this article, we evaluated the expression $-b + 8x$ when $b = 4$ and $x = -7$. We broke down the problem step by step, using simple language and clear explanations. We substituted the values of $b$ and $x$ into the expression, evaluated the terms, and combined them to get the final result. The final answer is $-60$.

Frequently Asked Questions

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Q: What is the value of $-b$ when $b = 4$?

A: The value of $-b$ is $-4$.

Q: What is the value of $8x$ when $x = -7$?

A: The value of $8x$ is $-56$.

Q: What is the final result when we evaluate the expression $-b + 8x$ when $b = 4$ and $x = -7$?

A: The final result is $-60$.

Tips and Tricks

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• When evaluating expressions, make sure to substitute the values correctly.
• When adding two negative numbers, remember that the result is a negative number.
• Practice evaluating expressions with different values to become more confident in your skills.

Related Topics

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• Evaluating expressions with variables
• Solving equations and inequalities
• Algebraic manipulations

Conclusion

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Evaluating expressions is a crucial skill in algebra. By following the steps outlined in this article, you can evaluate expressions with confidence. Remember to substitute values correctly, evaluate terms, and combine them to get the final result. With practice, you will become more proficient in evaluating expressions and solving equations and inequalities.

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Introduction

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In our previous article, we evaluated the expression $-b + 8x$ when $b = 4$ and $x = -7$. We broke down the problem step by step, using simple language and clear explanations. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

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

A: Evaluating an expression involves substituting values into the expression and simplifying it to get a numerical value. Solving an equation, on the other hand, involves finding the value of a variable that makes the equation true.

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

A: To evaluate an expression with multiple variables, you need to substitute the values of all the variables into the expression and simplify it. For example, if you have the expression $2x + 3y$ and you know that $x = 4$ and $y = 5$, you would substitute these values into the expression to get $2(4) + 3(5) = 8 + 15 = 23$.

Q: What is the order of operations when evaluating an expression?

A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression. The order of operations is:

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

Q: How do I evaluate an expression with negative numbers?

A: When evaluating an expression with negative numbers, remember that the negative sign can be moved to the other side of the expression. For example, if you have the expression $-2x$ and you know that $x = 3$, you would substitute this value into the expression to get $-2(3) = -6$.

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, on the other hand, is a value that does not change. For example, in the expression $2x + 3$, $x$ is a variable and $3$ is a constant.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, you need to follow the order of operations and simplify the expression. For example, if you have the expression $\frac{1}{2}x + \frac{1}{3}y$ and you know that $x = 4$ and $y = 5$, you would substitute these values into the expression to get $\frac{1}{2}(4) + \frac{1}{3}(5) = 2 + \frac{5}{3} = \frac{11}{3}$.

Tips and Tricks

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• When evaluating expressions, make sure to follow the order of operations.
• When working with negative numbers, remember that the negative sign can be moved to the other side of the expression.
• Practice evaluating expressions with different values to become more confident in your skills.

Related Topics

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• Evaluating expressions with variables
• Solving equations and inequalities
• Algebraic manipulations

Conclusion

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Evaluating expressions is a crucial skill in algebra. By following the steps outlined in this article, you can evaluate expressions with confidence. Remember to substitute values correctly, follow the order of operations, and simplify the expression to get the final result. With practice, you will become more proficient in evaluating expressions and solving equations and inequalities.