Algebra 2: Part 1 Flashcards

What is the first step in writing an algebraic expression for a real-world situation?

Identify the variable(s), coefficient(s), and constant(s) in the expression -13x + 45.

What is the expression for the total number of runners competing in a tournament with n schools?

Write the expression that represents the amount of money Anna earns from selling pies and cupcakes.

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

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

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

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

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

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

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.

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.