Algebra Basics Flashcards

Questions and Answers

What is the domain?

A statement formed by placing an equals symbol

The set of all values that a variable may represent (correct)

An equation that states a rule about a relationship

The set with no elements

What is an empty set?

The set with no elements, also known as the null set.

Define an equation.

A statement formed by placing an equals symbol between two numerical or variable expressions.

What does it mean to evaluate an expression?

To find the value of an expression. Signup and view all the answers

What is a formula?

An equation that states a rule about a relationship. Signup and view all the answers

What is an expression in mathematics?

An expression must contain numerals as well as operation signs and/or grouping symbols. Signup and view all the answers

What are grouping symbols?

Parentheses, brackets, and fraction bars used to clarify order of operations. Signup and view all the answers

What is a numerical expression?

An expression that represents a certain number. Signup and view all the answers

What is an open sentence?

A sentence containing one or more variables. Signup and view all the answers

What is the order of operations?

The order in which operations must be done when more than one operation is involved. Signup and view all the answers

What is a replacement set?

A set of values that are a solution to an open sentence. Signup and view all the answers

Define a set.

A collection of items. Signup and view all the answers

What are the sides of an equation?

The expressions to the left and right of the equals sign in an equation. Signup and view all the answers

What does simplifying an expression mean?

Replacing an expression containing variables with an equivalent expression containing fewer terms. Signup and view all the answers

What is a solution of an equation?

Any value of a variable that makes an open sentence true. Signup and view all the answers

What is a solution set?

The set of all solutions to a given open sentence. Signup and view all the answers

Define the term variable.

A symbol used to represent one or more numbers. Signup and view all the answers

What is a variable expression?

An expression that contains a variable. Signup and view all the answers

Study Notes

Algebra Basics

Domain: Represents all possible values a variable can take, essential in defining functions.
Empty Set: Also known as the null set, it contains no elements and is denoted by the symbol ∅.
Equation: A mathematical statement indicating equality, formed by linking two expressions with an equals sign.
Evaluate: The process of determining the numerical value of an expression by substituting variables with specific numbers.
Formula: A structured equation that expresses a particular relationship between different quantities.
Expression: Comprises numbers, operation signs (addition, subtraction, multiplication, division), and may include grouping symbols like parentheses or brackets.
Grouping Symbols: Tools such as parentheses (()), brackets ([]), and fraction bars that dictate the order of operations in expressions.
Numerical Expression: Represents a single number using numerals and arithmetical operations.
Open Sentence: A mathematical statement containing one or more variables, which requires specific values to evaluate its truthfulness.
Order of Operations: A guideline that dictates the sequence for performing operations in mathematical expressions to ensure consistency, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Replacement Set: A collection of values assigned as potential solutions for an open sentence, used to determine truthfulness.
Set: A systematic compilation of distinct items or elements, typically denoted by curly braces {}.
Sides of an Equation: The expressions found on either side of the equals sign; crucial for solving equations.
Simplifying an Expression: Involves transforming a complex expression into a simpler form with less complexity, reducing the number of terms.
Solution of an Equation: Any variable value that satisfies an open sentence, making it true.
Solution Set: The complete collection of all valid solutions that satisfy a particular open sentence or equation.
Variable: A symbolic representation (like x or y) used to denote one or more unknown numerical values.
Variable Expression: An expression that includes at least one variable, allowing it to represent a range of values.

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Test your knowledge of basic algebra concepts with these flashcards. Each card presents a key term along with its definition, covering essential vocabulary like domain, empty set, equation, and more. Perfect for beginners looking to strengthen their understanding of algebra fundamentals.