Algebra 2: Part 1 Flashcards
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Questions and Answers

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.

Variable: x, Coefficient: -13, Constant: 45

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.

<p>$10p + $2c</p> Signup and view all the answers

What is the total amount Ben spent at the fair if he rode r rides?

<p>$3r + $10</p> Signup and view all the answers

What does it mean to have the simplified form of an expression?

<p>An equivalent expression that's easier to use than the original expression.</p> Signup and view all the answers

The first step in the order of operations is to simplify inside any ______ or grouping symbols.

<p>parentheses</p> Signup and view all the answers

What is the first operation applied to the expression 2(x + 3) + 4(x - 1)?

<p>Multiplication using the distributive property.</p> Signup and view all the answers

What is the result of simplifying the expression 2(x + 3) + 4(x - 1)?

<p>6x + 2</p> Signup and view all the answers

What is the first step in simplifying the expression 3(x + 2x) + 4(x + 1)?

<p>Simplify inside the first parentheses.</p> Signup and view all the answers

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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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.

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