Evaluate 10.2 X + 9.4 Y 10.2x + 9.4y 10.2 X + 9.4 Y When X = 2 X = 2 X = 2 And Y = 3 Y = 3 Y = 3 . 10.2 ( 2 ) + 9.4 ( 3 10.2(2) + 9.4(3 10.2 ( 2 ) + 9.4 ( 3 ]

Mar 13, 2025 by ADMIN 159 views

Evaluating Algebraic Expressions: A Step-by-Step Guide

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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 focus on evaluating the expression $10.2x + 9.4y$ when $x = 2$ and $y = 3$ . We will break down the process into manageable steps and provide a clear explanation of each step.

Understanding the Expression

The given expression is $10.2x + 9.4y$ . This is a linear expression, which means it can be written in the form $ax + by$ , where $a$ and $b$ are constants, and $x$ and $y$ are variables. In this case, $a = 10.2$ and $b = 9.4$ .

Substituting the Values of x and y

To evaluate the expression, we need to substitute the values of $x$ and $y$ into the expression. We are given that $x = 2$ and $y = 3$ . Substituting these values into the expression, we get:

$10.2(2) + 9.4(3)$

Evaluating the Expression

Now that we have substituted the values of $x$ and $y$ , we can evaluate the expression. To do this, we need to follow the order of operations (PEMDAS):

Multiply $10.2$ by $2$ : $10.2(2) = 20.4$
Multiply $9.4$ by $3$ : $9.4(3) = 28.2$
Add the results of the two multiplications: $20.4 + 28.2 = 48.6$

Conclusion

In this article, we evaluated the expression $10.2x + 9.4y$ when $x = 2$ and $y = 3$ . We broke down the process into manageable steps and provided a clear explanation of each step. By following the order of operations, we were able to evaluate the expression and find the result.

Tips and Tricks

When evaluating algebraic expressions, it's essential to follow the order of operations (PEMDAS).
Make sure to substitute the values of variables into the expression correctly.
Use parentheses to group numbers and variables correctly.
Check your work by plugging in the values of variables into the expression.

Real-World Applications

Evaluating algebraic expressions has numerous real-world applications. For example:

In finance, algebraic expressions are used to calculate interest rates and investment returns.
In science, algebraic expressions are used to model population growth and chemical reactions.
In engineering, algebraic expressions are used to design and optimize systems.

Common Mistakes

Not following the order of operations (PEMDAS).
Substituting the values of variables incorrectly.
Not using parentheses to group numbers and variables correctly.

Final Thoughts

Evaluating algebraic expressions is a crucial skill that has numerous real-world applications. By following the order of operations and substituting the values of variables correctly, we can evaluate expressions and find the result. Remember to check your work and use parentheses to group numbers and variables correctly.

Additional Resources

Khan Academy: Algebra
Mathway: Algebra Calculator
Wolfram Alpha: Algebra Solver

Frequently Asked Questions

Q: What is the order of operations (PEMDAS)? A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I evaluate an algebraic expression? A: To evaluate an algebraic expression, follow the order of operations (PEMDAS) and substitute the values of variables into the expression correctly.
Q: What are some common mistakes to avoid when evaluating algebraic expressions? A: Some common mistakes to avoid include not following the order of operations (PEMDAS), substituting the values of variables incorrectly, and not using parentheses to group numbers and variables correctly.

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Introduction

Evaluating algebraic expressions is a crucial skill that has numerous real-world applications. In our previous article, we provided a step-by-step guide on how to evaluate the expression $10.2x + 9.4y$ when $x = 2$ and $y = 3$ . In this article, we will provide a Q&A guide to help you better understand the concept of evaluating algebraic expressions.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

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

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, follow the order of operations (PEMDAS) and substitute the values of variables into the expression correctly.

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

A: Some common mistakes to avoid include not following the order of operations (PEMDAS), substituting the values of variables incorrectly, and not using parentheses to group numbers and variables correctly.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, combine like terms and eliminate any unnecessary parentheses.

Q: What is a like term?

A: A like term is a term that has the same variable and exponent. For example, $2x$ and $3x$ are like terms.

Q: How do I factor an algebraic expression?

A: To factor an algebraic expression, look for common factors and group them together.

Q: What is a common factor?

A: A common factor is a factor that is common to all terms in an expression. For example, in the expression $2x + 4x$ , the common factor is $2x$ .

Q: How do I solve an algebraic equation?

A: To solve an algebraic equation, isolate the variable by performing inverse operations.

Q: What is an inverse operation?

A: An inverse operation is an operation that undoes the effect of another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I graph an algebraic function?

A: To graph an algebraic function, use a graphing calculator or software to visualize the function.

Q: What is a graphing calculator?

A: A graphing calculator is a calculator that can graph algebraic functions and perform other mathematical operations.

Q: How do I use a graphing calculator?

A: To use a graphing calculator, enter the function into the calculator and use the graphing features to visualize the function.