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Questions and Answers
What is the first step in writing an algebraic expression for a real-world situation?
What is the first step in writing an algebraic expression for a real-world situation?
Identify any unknown values and assign variables to them.
Identify the variable(s), coefficient(s), and constant(s) in the expression -13x + 45.
Identify the variable(s), coefficient(s), and constant(s) in the expression -13x + 45.
Variable: x, Coefficient: -13, Constant: 45
What is the expression for the total number of runners competing in a tournament with n schools?
What is the expression for the total number of runners competing in a tournament with n schools?
12n
Write the expression that represents the amount of money Anna earns from selling pies and cupcakes.
Write the expression that represents the amount of money Anna earns from selling pies and cupcakes.
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What is the total amount Ben spent at the fair if he rode r rides?
What is the total amount Ben spent at the fair if he rode r rides?
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What does it mean to have the simplified form of an expression?
What does it mean to have the simplified form of an expression?
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The first step in the order of operations is to simplify inside any ______ or grouping symbols.
The first step in the order of operations is to simplify inside any ______ or grouping symbols.
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What is the first operation applied to the expression 2(x + 3) + 4(x - 1)?
What is the first operation applied to the expression 2(x + 3) + 4(x - 1)?
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What is the result of simplifying the expression 2(x + 3) + 4(x - 1)?
What is the result of simplifying the expression 2(x + 3) + 4(x - 1)?
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What is the first step in simplifying the expression 3(x + 2x) + 4(x + 1)?
What is the first step in simplifying the expression 3(x + 2x) + 4(x + 1)?
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Study Notes
Writing Algebraic Expressions
- Identify unknown values in real-world situations and assign variables.
- Determine necessary operations to accurately describe the situation.
Coefficients, Variables, and Constants
- Expression: -13x + 45
- Variable: x
- Coefficient: -13
- Constant: 45
- Expression: 12 - y
- Variable: y
- Coefficient: -1
- Constant: 12
- Expression: 2y + 3x - 6
- Variables: x, y
- Coefficients: 2, 3
- Constant: -6
- Expression: 24 - 56m + 103
- Variable: m
- Coefficient: -56
- Constants: 24, 103
- Expression: 3.25 + 0.5p
- Variable: p
- Coefficient: 0.5
- Constant: 3.25
Total Number of Runners
- Unknown value for number of schools competing: n.
- Total runners expression: 12n (12 runners per school).
Earnings from Bake Sale
- Variables for unknowns: p (pies sold), c (cupcakes sold).
- Earnings from pies: $10p; from cupcakes: $2c.
- Total earnings expression: $10p + $2c.
Expenses at the Fair
- Variable for rides: r.
- Cost for rides: $3r; entrance fee is $10.
- Total spending expression: $3r + $10.
Simplifying Expressions
- Simplification results in equivalent expressions that are often shorter and easier to use.
- May involve combining like terms and applying the distributive property.
- Example simplification: 2(x+3) + 4(x-1) requires distributive property and combining like terms.
Order of Operations
- Step 1: Simplify inside parentheses.
- Step 2: Evaluate exponents.
- Step 3: Perform multiplication and division from left to right.
- Step 4: Perform addition and subtraction from left to right.
Example of Expression Simplification
- Example: Simplify 2(x + 3) + 4(x - 1).
- Apply distributive rule: 2x + 6 + 4x - 4.
- Combine like terms: (2 + 4)x + 2 leads to 6x + 2.
Another Example of Simplification
- Example: Simplify 3(x + 2x) + 4(x + 1).
- Simplify first parentheses: 3(3x) + 4(x + 1).
- Apply distributive rule: 9x + 4x + 4.
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Description
Test your understanding of algebraic expressions with our flashcards on identifying coefficients, variables, and constants. Learn how to assign variables to real-world situations and the operations needed to create expressions. Perfect for Algebra 2 students preparing for exams.
