Evaluate 3 ( 10 X + Y ) + 2 X + 7 Y 3(10x + Y) + 2x + 7y 3 ( 10 X + Y ) + 2 X + 7 Y For X = 1 X = 1 X = 1 And Y = 2 Y = 2 Y = 2 .

$$$$$$

Introduction

In this article, we will evaluate the expression $3(10x + y) + 2x + 7y$ for the given values of $x = 1$ and $y = 2$. This involves substituting the values of $x$ and $y$ into the expression and simplifying it to obtain the final result.

Understanding the Expression

The given expression is a linear combination of the variables $x$ and $y$. It consists of two terms: $3(10x + y)$ and $2x + 7y$. The first term is a product of a constant $3$ and a linear expression $10x + y$, while the second term is a linear expression in $x$ and $y$.

Substituting the Values of $x$ and $y$

To evaluate the expression, we need to substitute the values of $x = 1$ and $y = 2$ into the expression. This involves replacing each occurrence of $x$ with $1$ and each occurrence of $y$ with $2$.

Evaluating the Expression

Let's substitute the values of $x$ and $y$ into the expression:

$$3(10x + y) + 2x + 7y$$

$$= 3(10(1) + 2) + 2(1) + 7(2)$$

$$= 3(12) + 2 + 14$$

$$= 36 + 2 + 14$$

$$= 52$$

Conclusion

In this article, we evaluated the expression $3(10x + y) + 2x + 7y$ for the given values of $x = 1$ and $y = 2$. We substituted the values of $x$ and $y$ into the expression and simplified it to obtain the final result, which is $52$.

Step-by-Step Solution

Here's a step-by-step solution to the problem:

1. Substitute the values of $x$ and $y$ into the expression:

$$3(10x + y) + 2x + 7y$$

$$= 3(10(1) + 2) + 2(1) + 7(2)$$

2. Simplify the expression inside the parentheses:

$$= 3(12) + 2 + 14$$

3. Multiply the constant $3$ by the expression inside the parentheses:

$$= 36 + 2 + 14$$

4. Add the constants together:

$$= 52$$

Frequently Asked Questions

• What is the value of $x$? $x = 1$
• What is the value of $y$? $y = 2$
• How do I evaluate the expression $3(10x + y) + 2x + 7y$ for $x = 1$ and $y = 2$? To evaluate the expression, substitute the values of $x$ and $y$ into the expression and simplify it.

Final Answer

The final answer is $\boxed{52}$.

Introduction

Evaluating algebraic expressions is a fundamental concept in mathematics that involves substituting values into an expression and simplifying it to obtain a final result. In this article, we will provide a Q&A guide on evaluating algebraic expressions, including common mistakes to avoid and tips for simplifying expressions.

Q&A: Evaluating Algebraic Expressions

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values into the expression and simplify it using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

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

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in 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 simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary operations. Like terms are terms that have the same variable raised to the same power.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, 2x + 4x can be combined to get 6x.

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

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

• Not following the order of operations (PEMDAS)
• Not combining like terms
• Not eliminating unnecessary operations
• Not checking for errors in the expression

Q: How do I check for errors in an algebraic expression?

A: To check for errors in an algebraic expression, you need to:

• Read the expression carefully to ensure that it is correct
• Check that the order of operations (PEMDAS) is followed
• Check that like terms are combined correctly
• Check that unnecessary operations are eliminated

Tips for Evaluating Algebraic Expressions

• Always follow the order of operations (PEMDAS)
• Combine like terms to simplify the expression
• Eliminate unnecessary operations to simplify the expression
• Check for errors in the expression before evaluating it
• Use a calculator or computer program to check your work if necessary

Conclusion

Evaluating algebraic expressions is a fundamental concept in mathematics that involves substituting values into an expression and simplifying it to obtain a final result. By following the order of operations (PEMDAS) and combining like terms, you can simplify algebraic expressions and obtain accurate results. Remember to check for errors in the expression before evaluating it, and use a calculator or computer program to check your work if necessary.

Frequently Asked Questions

• What is an algebraic expression?
• How do I evaluate an algebraic expression?
• What is the order of operations (PEMDAS)?
• How do I simplify an algebraic expression?
• What are like terms?
• How do I combine like terms?
• What are common mistakes to avoid when evaluating algebraic expressions?
• How do I check for errors in an algebraic expression?

Final Answer

The final answer is that evaluating algebraic expressions is a fundamental concept in mathematics that involves substituting values into an expression and simplifying it to obtain a final result. By following the order of operations (PEMDAS) and combining like terms, you can simplify algebraic expressions and obtain accurate results.