Simplify The Expression:$\[-17 - 3(2x + 13) + 24\\]
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Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying the given expression: ${-17 - 3(2x + 13) + 24}$. We will break down the expression into smaller parts, apply the order of operations, and simplify it step by step.
Understanding the Expression
The given expression is a combination of constants and variables. It consists of three main parts:
- A constant term: ${-17}$
- A term with a variable: ${-3(2x + 13)}$
- Another constant term: ${24}$
Applying the Order of Operations
The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Step 1: Evaluate the Expression Inside the Parentheses
The expression inside the parentheses is ${2x + 13}$. We will leave it as is for now and come back to it later.
Step 2: Multiply the Term Outside the Parentheses
The term outside the parentheses is $-3}$. We will multiply it by the expression inside the parentheses$.
Step 3: Simplify the Expression
Now that we have multiplied the term outside the parentheses, we can simplify the expression:
Conclusion
Simplifying algebraic expressions is an essential skill in mathematics. By following the order of operations and applying the rules of algebra, we can simplify complex expressions and arrive at a final answer. In this article, we simplified the expression ${-17 - 3(2x + 13) + 24}$ step by step, using the order of operations and applying the rules of algebra.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- 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, follow these steps:
- Evaluate any expressions inside parentheses.
- Multiply any terms outside the parentheses by the expression inside the parentheses.
- Combine like terms.
- Apply the order of operations.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. For example, ${2x}$ and ${3x}$ are like terms because they both have the variable ${x}$ raised to the power of 1.
Final Answer
The final answer is ${-6x - 32}$.
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Introduction
Algebraic expressions are a fundamental concept in mathematics, and understanding them is crucial for success in various fields. In this article, we will provide a comprehensive Q&A guide to algebraic expressions, covering various topics and concepts.
Frequently Asked Questions
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.
Q: What are the basic components of an algebraic expression?
A: The basic components of an algebraic expression are:
- Variables: Letters or symbols that represent unknown values.
- Constants: Numbers that do not change value.
- Mathematical operations: Addition, subtraction, multiplication, and division.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- 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, follow these steps:
- Evaluate any expressions inside parentheses.
- Multiply any terms outside the parentheses by the expression inside the parentheses.
- Combine like terms.
- Apply the order of operations.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. For example, ${2x}$ and ${3x}$ 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, add or subtract the coefficients of the like terms. For example, ${2x + 3x}$ can be combined as ${5x}$.
Q: What is the difference between a variable and a constant?
A: A variable is a letter or symbol that represents an unknown value, while a constant is a number that does not change value.
Q: Can I have multiple variables in an algebraic expression?
A: Yes, you can have multiple variables in an algebraic expression. For example, ${2x + 3y}$ is an algebraic expression with two variables, ${x}$ and ${y}$.
Q: How do I evaluate an algebraic expression with multiple variables?
A: To evaluate an algebraic expression with multiple variables, substitute the values of the variables into the expression and simplify.
Q: What is the purpose of algebraic expressions?
A: Algebraic expressions are used to represent mathematical relationships between variables and constants. They are used in various fields, including science, engineering, economics, and finance.
Q: Can I use algebraic expressions to solve real-world problems?
A: Yes, algebraic expressions can be used to solve real-world problems. They are used to model and analyze complex systems, make predictions, and optimize solutions.
Conclusion
Algebraic expressions are a fundamental concept in mathematics, and understanding them is crucial for success in various fields. By following the order of operations, combining like terms, and evaluating expressions, you can simplify complex algebraic expressions and arrive at a final answer. In this article, we provided a comprehensive Q&A guide to algebraic expressions, covering various topics and concepts.
Final Answer
The final answer is that algebraic expressions are a powerful tool for representing mathematical relationships between variables and constants. By understanding and applying the concepts and techniques covered in this article, you can simplify complex algebraic expressions and solve real-world problems.
Additional Resources
- Algebraic Expressions Tutorial
- Algebraic Expressions Practice Problems
- Algebraic Expressions Online Course
Related Articles
Tags
- Algebraic Expressions
- Simplifying Algebraic Expressions
- Evaluating Algebraic Expressions
- Combining Like Terms
- Order of Operations
- Variables
- Constants
- Mathematical Operations