Evaluate The Expression When $a = 4$ And $c = -7$. − A + 9 C -a + 9c − A + 9 C

Mar 12, 2025 by ADMIN 83 views

Evaluate the Expression: A Step-by-Step Guide

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Introduction

In mathematics, expressions are a combination of variables, constants, and mathematical operations. Evaluating an expression involves substituting the given values of variables and performing the operations to obtain the final result. In this article, we will evaluate the expression $-a + 9c$ when $a = 4$ and $c = -7$ .

Understanding the Expression

The given expression is $-a + 9c$ . This expression consists of two terms: $-a$ and $9c$ . The first term is the negative of the variable $a$ , and the second term is nine times the variable $c$ .

Substituting the Given Values

We are given that $a = 4$ and $c = -7$ . To evaluate the expression, we need to substitute these values into the expression.

Step 1: Substitute the Value of $a$

Substituting $a = 4$ into the expression, we get:

-4 + 9c

Step 2: Substitute the Value of $c$

Substituting $c = -7$ into the expression, we get:

-4 + 9(-7)

Evaluating the Expression

Now that we have substituted the values of $a$ and $c$ , we can evaluate the expression.

Step 3: Multiply 9 and $-7$

Multiplying 9 and $-7$ , we get:

-63

Step 4: Add $-4$ and $-63$

Adding $-4$ and $-63$ , we get:

-67

Conclusion

Therefore, the value of the expression $-a + 9c$ when $a = 4$ and $c = -7$ is $-67$ .

Final Answer

The final answer is $\boxed{-67}$ .

Frequently Asked Questions

Q: What is the value of the expression $-a + 9c$ when $a = 4$ and $c = -7$ ?

A: The value of the expression $-a + 9c$ when $a = 4$ and $c = -7$ is $-67$ .

Q: How do I evaluate an expression in mathematics?

A: To evaluate an expression, you need to substitute the given values of variables and perform the operations to obtain the final result.

Q: What are the steps involved in evaluating an expression?

A: The steps involved in evaluating an expression are:

Substitute the given values of variables into the expression.
Perform the operations to obtain the final result.

References

[1] "Algebra" by Michael Artin
[2] "Calculus" by Michael Spivak
[3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

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Introduction

Evaluating expressions is a fundamental concept in mathematics. It involves substituting the given values of variables and performing the operations to obtain the final result. In this article, we will provide a Q&A guide on evaluating expressions, covering various topics and scenarios.

Q: What is an expression in mathematics?

A: An expression in mathematics is a combination of variables, constants, and mathematical operations. It can be a simple expression like $2x + 3$ or a complex expression like $x^2 + 2xy + y^2$ .

Q: How do I evaluate an expression in mathematics?

A: To evaluate an expression, you need to substitute the given values of variables and perform the operations to obtain the final result. The steps involved in evaluating an expression are:

Substitute the given values of variables into the expression.
Perform the operations to obtain the final result.

Q: What are the different types of expressions in mathematics?

A: There are several types of expressions in mathematics, including:

Algebraic expressions: These are expressions that involve variables and constants, such as $2x + 3$ .
Trigonometric expressions: These are expressions that involve trigonometric functions, such as $\sin x + \cos x$ .
Exponential expressions: These are expressions that involve exponential functions, such as $2^x + 3^x$ .
Logarithmic expressions: These are expressions that involve logarithmic functions, such as $\log x + \log y$ .

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 and perform the operations to obtain the final result. For example, if you have the expression $2x + 3y + 4z$ and you are given the values $x = 2$ , $y = 3$ , and $z = 4$ , you would substitute these values into the expression and perform the operations to obtain the final result.

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

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

Not substituting the given values of variables: Make sure to substitute the given values of variables into the expression.
Not performing the operations in the correct order: Make sure to perform the operations in the correct order, following the order of operations (PEMDAS).
Not simplifying the expression: Make sure to simplify the expression after performing the operations.

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

A: To evaluate an expression with negative numbers, you need to follow the rules of arithmetic with negative numbers. For example, if you have the expression $-2x + 3y$ and you are given the values $x = -2$ and $y = 3$ , you would substitute these values into the expression and perform the operations to obtain the final result.

Q: What are some real-world applications of evaluating expressions?

A: Evaluating expressions has many real-world applications, including:

Science and engineering: Evaluating expressions is used to model real-world phenomena and make predictions.
Finance: Evaluating expressions is used to calculate interest rates, investment returns, and other financial metrics.
Computer science: Evaluating expressions is used to write algorithms and solve problems.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, you need to follow the rules of arithmetic with fractions. For example, if you have the expression $\frac{1}{2}x + \frac{3}{4}y$ and you are given the values $x = 2$ and $y = 4$ , you would substitute these values into the expression and perform the operations to obtain the final result.

Q: What are some tips for evaluating expressions?

A: Some tips for evaluating expressions include:

Read the expression carefully: Make sure to read the expression carefully and understand what it means.
Substitute the given values of variables: Make sure to substitute the given values of variables into the expression.
Perform the operations in the correct order: Make sure to perform the operations in the correct order, following the order of operations (PEMDAS).
Simplify the expression: Make sure to simplify the expression after performing the operations.

Conclusion

Evaluating expressions is a fundamental concept in mathematics. It involves substituting the given values of variables and performing the operations to obtain the final result. By following the steps involved in evaluating an expression and avoiding common mistakes, you can evaluate expressions with confidence.

Introduction

Understanding the Expression

Substituting the Given Values

Step 1: Substitute the Value of aaa

Step 2: Substitute the Value of ccc

Evaluating the Expression

Step 3: Multiply 9 and −7-7−7

Step 4: Add −4-4−4 and −63-63−63

Conclusion

Final Answer

Frequently Asked Questions

Q: What is the value of the expression −a+9c-a + 9c−a+9c when a=4a = 4a=4 and c=−7c = -7c=−7?

Q: How do I evaluate an expression in mathematics?

Q: What are the steps involved in evaluating an expression?

Related Topics

References

Introduction

Q: What is an expression in mathematics?

Q: How do I evaluate an expression in mathematics?

Q: What are the different types of expressions in mathematics?

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

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

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

Q: What are some real-world applications of evaluating expressions?

Q: How do I evaluate an expression with fractions?

Q: What are some tips for evaluating expressions?

Conclusion

Step 1: Substitute the Value of $a$

Step 2: Substitute the Value of $c$

Step 3: Multiply 9 and $-7$

Step 4: Add $-4$ and $-63$

Q: What is the value of the expression $-a + 9c$ when $a = 4$ and $c = -7$ ?