If $a=6, B=3$, And $c=7$, Evaluate The Following Expression: $\frac{3(4a-3c)}{c-4}$A. 147 B. 84 C. \$\frac{1}{3}$[/tex\] D. 3

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students and professionals alike. In this article, we will guide you through the process of evaluating a given algebraic expression using the values of the variables provided.

The Expression to Evaluate

The given expression is:

3(4a−3c)c−4\frac{3(4a-3c)}{c-4}

We are provided with the values of the variables aa, bb, and cc as follows:

a=6,b=3,c=7a=6, b=3, c=7

Step 1: Substitute the Values of the Variables

To evaluate the expression, we need to substitute the values of the variables aa, bb, and cc into the expression.

3(4a−3c)c−4=3(4(6)−3(7))7−4\frac{3(4a-3c)}{c-4} = \frac{3(4(6)-3(7))}{7-4}

Step 2: Simplify the Expression

Now, we need to simplify the expression by performing the arithmetic operations inside the parentheses.

3(24−21)3=3(3)3\frac{3(24-21)}{3} = \frac{3(3)}{3}

Step 3: Evaluate the Expression

Finally, we can evaluate the expression by performing the division.

3(3)3=3\frac{3(3)}{3} = 3

Conclusion

Therefore, the value of the given expression is 33.

Why Choose This Approach?

This approach is useful for evaluating algebraic expressions because it involves breaking down the expression into smaller parts, substituting the values of the variables, and simplifying the expression step by step. This approach helps to ensure that the expression is evaluated correctly and reduces the likelihood of errors.

Common Mistakes to Avoid

When evaluating algebraic expressions, it's essential to avoid common mistakes such as:

  • Not substituting the values of the variables correctly
  • Not simplifying the expression properly
  • Not performing the arithmetic operations correctly

Real-World Applications

Evaluating algebraic expressions has numerous real-world applications, including:

  • Science and engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
  • Economics: Algebraic expressions are used to model economic systems, such as supply and demand curves.
  • Computer science: Algebraic expressions are used to model algorithms and data structures.

Final Thoughts

Evaluating algebraic expressions is a crucial skill that requires attention to detail and a step-by-step approach. By following the approach outlined in this article, you can ensure that you evaluate algebraic expressions correctly and accurately. Remember to avoid common mistakes and apply the concepts learned to real-world applications.

Frequently Asked Questions

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and arithmetic operations.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the values of the variables, simplify the expression, and perform the arithmetic operations.

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

A: Some common mistakes to avoid include not substituting the values of the variables correctly, not simplifying the expression properly, and not performing the arithmetic operations correctly.

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

A: Evaluating algebraic expressions has numerous real-world applications, including science and engineering, economics, and computer science.

Q: Why is it essential to evaluate algebraic expressions correctly?

A: Evaluating algebraic expressions correctly is essential because it helps to ensure that mathematical models are accurate and reliable, which is critical in various fields, including science, engineering, and economics.

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Introduction

Evaluating algebraic expressions is a crucial skill that requires attention to detail and a step-by-step approach. In this article, we will provide a comprehensive Q&A guide to help you understand the concepts and techniques involved in evaluating algebraic expressions.

Q&A Guide

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and arithmetic operations.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to follow these steps:

  1. Substitute the values of the variables into the expression.
  2. Simplify the expression by combining like terms and performing arithmetic operations.
  3. Perform the arithmetic operations in the correct order (PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

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

A: Some common mistakes to avoid include:

  • Not substituting the values of the variables correctly
  • Not simplifying the expression properly
  • Not performing the arithmetic operations correctly
  • Not following the order of operations (PEMDAS)

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

A: Evaluating algebraic expressions has numerous real-world applications, including:

  • Science and engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
  • Economics: Algebraic expressions are used to model economic systems, such as supply and demand curves.
  • Computer science: Algebraic expressions are used to model algorithms and data structures.

Q: Why is it essential to evaluate algebraic expressions correctly?

A: Evaluating algebraic expressions correctly is essential because it helps to ensure that mathematical models are accurate and reliable, which is critical in various fields, including science, engineering, and economics.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

  1. Combine like terms by adding or subtracting coefficients of the same variable.
  2. Perform arithmetic operations, such as multiplication and division.
  3. Remove any unnecessary parentheses or brackets.

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

A: The order of operations (PEMDAS) is a set of rules that dictates the order in which arithmetic operations should be performed. The acronym PEMDAS stands for:

  • P: Parentheses
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction

Q: How do I evaluate an expression with exponents?

A: To evaluate an expression with exponents, you need to follow these steps:

  1. Evaluate the expression inside the parentheses.
  2. Raise the base to the power of the exponent.
  3. Simplify the expression by combining like terms.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

  • Linear expressions: ax+bax + b
  • Quadratic expressions: ax2+bx+cax^2 + bx + c
  • Polynomial expressions: anxn+an−1xn−1+…+a1x+a0a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0

Q: How do I evaluate an expression with variables in the denominator?

A: To evaluate an expression with variables in the denominator, you need to follow these steps:

  1. Simplify the expression by combining like terms.
  2. Perform arithmetic operations, such as multiplication and division.
  3. Remove any unnecessary parentheses or brackets.

Conclusion

Evaluating algebraic expressions is a crucial skill that requires attention to detail and a step-by-step approach. By following the Q&A guide provided in this article, you can ensure that you evaluate algebraic expressions correctly and accurately. Remember to avoid common mistakes and apply the concepts learned to real-world applications.

Final Thoughts

Evaluating algebraic expressions is a fundamental concept in mathematics, and it has numerous real-world applications. By mastering the techniques and concepts outlined in this article, you can become proficient in evaluating algebraic expressions and apply them to various fields, including science, engineering, and economics.

Frequently Asked Questions

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

A: An algebraic expression is a mathematical expression that contains variables, constants, and arithmetic operations, while an equation is a statement that two expressions are equal.

Q: How do I solve an equation with variables on both sides?

A: To solve an equation with variables on both sides, you need to follow these steps:

  1. Add or subtract the same value to both sides of the equation.
  2. Multiply or divide both sides of the equation by the same value.
  3. Simplify the equation by combining like terms.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation with a linear expression on one side, while a quadratic equation is an equation with a quadratic expression on one side.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to follow these steps:

  1. Find the x-intercept by setting y = 0.
  2. Find the y-intercept by setting x = 0.
  3. Plot the points on a coordinate plane.
  4. Draw a line through the points.

Q: What is the difference between a function and a relation?

A: A function is a relation where each input corresponds to exactly one output, while a relation is a set of ordered pairs that may have multiple inputs corresponding to the same output.