Evaluate The Expression $2a - 3b + 7$ When $a = 14$ And $b = 6$.Enter Your Answer With Numbers And Decimals Only.

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Introduction

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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 $2a - 3b + 7$ when $a = 14$ and $b = 6$. We will break down the process into manageable steps, making it easy to understand and follow.

Understanding Algebraic Expressions

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An algebraic expression is a mathematical statement that combines variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using symbols and mathematical notation. Algebraic expressions can be simple or complex, and they can be used to solve equations, inequalities, and other mathematical problems.

Types of Algebraic Expressions

Variables and Constants

In an algebraic expression, variables are represented by letters, such as $a$ and $b$, while constants are represented by numbers, such as $2$ and $7$. Variables can take on different values, while constants remain the same.

Mathematical Operations

Algebraic expressions involve various mathematical operations, including addition, subtraction, multiplication, and division. These operations can be combined in different ways to create more complex expressions.

Evaluating the Expression $2a - 3b + 7$

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To evaluate the expression $2a - 3b + 7$, we need to substitute the given values of $a$ and $b$ into the expression. We will then simplify the expression to obtain the final result.

Step 1: Substitute the Values of $a$ and $b$

Substituting $a = 14$ and $b = 6$

We will substitute the values of $a$ and $b$ into the expression $2a - 3b + 7$. This gives us:

$2(14) - 3(6) + 7$

Step 2: Simplify the Expression

Multiplying and Subtracting

We will now simplify the expression by multiplying and subtracting the terms.

$2(14) = 28$ $3(6) = 18$ $28 - 18 = 10$ $10 + 7 = 17$

Step 3: Final Result

Evaluating the Expression

The final result of evaluating the expression $2a - 3b + 7$ when $a = 14$ and $b = 6$ is:

$17$

Conclusion

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Evaluating algebraic expressions is an essential skill in mathematics, and it requires a clear understanding of variables, constants, and mathematical operations. By following the steps outlined in this article, we can easily evaluate the expression $2a - 3b + 7$ when $a = 14$ and $b = 6$. We hope that this article has provided a helpful guide for students and professionals alike.

Frequently Asked Questions

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Q: What is an algebraic expression?

A: An algebraic expression is a mathematical statement that combines variables, constants, and mathematical operations.

Q: What are variables and constants in an algebraic expression?

A: Variables are represented by letters, such as $a$ and $b$, while constants are represented by numbers, such as $2$ and $7$.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values of the variables into the expression and simplify the expression using mathematical operations.

Further Reading

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If you want to learn more about algebraic expressions and how to evaluate them, we recommend the following resources:

• Algebraic Expressions
• Evaluating Algebraic Expressions
• Algebraic Expressions and Equations

We hope that this article has provided a helpful guide for evaluating algebraic expressions. If you have any questions or need further clarification, please don't hesitate to ask.

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Introduction

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Evaluating algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of variables, constants, and mathematical operations. In this article, we will provide a Q&A guide to help students and professionals alike understand and evaluate algebraic expressions.

Q&A: Evaluating Algebraic Expressions

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Q: What is an algebraic expression?

A: An algebraic expression is a mathematical statement that combines variables, constants, and mathematical operations.

Q: What are variables and constants in an algebraic expression?

A: Variables are represented by letters, such as $a$ and $b$, while constants are represented by numbers, such as $2$ and $7$.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values of the variables into the expression and simplify the expression using mathematical operations.

Q: What are the steps to evaluate an algebraic expression?

A: The steps to evaluate an algebraic expression are:

1. Substitute the given values of the variables into the expression.
2. Simplify the expression using mathematical operations.
3. Evaluate the expression to obtain the final result.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

• $2x + 3$
• $x^2 + 4x + 5$
• $3x - 2$

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and perform mathematical operations.

Q: What are like terms in an algebraic expression?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $3x$ are like terms.

Q: How do I combine like terms in an algebraic expression?

A: To combine like terms, you need to add or subtract the coefficients of the like terms.

Q: What are the coefficients of a term in an algebraic expression?

A: The coefficients of a term are the numbers that multiply the variable. For example, in the term $2x$, the coefficient is $2$.

Q: How do I evaluate an algebraic expression with exponents?

A: To evaluate an algebraic expression with exponents, you need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division expressions from left to right.
4. Evaluate any addition and subtraction expressions from left to right.

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

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an algebraic expression. The acronym PEMDAS stands for:

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

Conclusion

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Evaluating algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of variables, constants, and mathematical operations. By following the steps outlined in this article, you can easily evaluate algebraic expressions and simplify complex expressions. We hope that this Q&A guide has provided a helpful resource for students and professionals alike.

Frequently Asked Questions

---

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical statement that combines variables, constants, and mathematical operations.

Q: What are variables and constants in an algebraic expression?

A: Variables are represented by letters, such as $a$ and $b$, while constants are represented by numbers, such as $2$ and $7$.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values of the variables into the expression and simplify the expression using mathematical operations.

Further Reading

---

If you want to learn more about algebraic expressions and how to evaluate them, we recommend the following resources:

• Algebraic Expressions
• Evaluating Algebraic Expressions
• Algebraic Expressions and Equations

We hope that this article has provided a helpful guide for evaluating algebraic expressions. If you have any questions or need further clarification, please don't hesitate to ask.