Algebra Chapter 1: Equations and Inequalities Vocabulary

Questions and Answers

What does 'absolute value' represent?

A mathematical sentence expressing the relationship between quantities

An expression which contains at least one variable

Two separate inequalities graphed on the same coordinate plane

The number of units between a number and zero (correct)

What is an algebraic expression?

An expression which contains at least one variable

Define compound inequality.

Two separate inequalities which are graphed on the same coordinate plane.

What is an empty set?

An equation that has no real answer has this as its solution set. Signup and view all the answers

Provide an example of an equation.

-5x^2=-125 Signup and view all the answers

Define a formula.

A mathematical sentence which expresses the relationship between certain quantities. Signup and view all the answers

What are integers?

Whole numbers with either a positive or negative sign. Signup and view all the answers

The graph of a compound inequality containing the word 'and' can be called the ________ of the graphs of the two separate inequalities.

intersection Signup and view all the answers

What are irrational numbers?

Numbers which cannot be written in the form of a over b. Signup and view all the answers

Define natural numbers.

Positive whole numbers which do not contain zero. Signup and view all the answers

What is an open sentence?

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

What is the order of operations?

The order in which you solve expressions or equations containing more than one operation. Signup and view all the answers

What are rational numbers?

A number that can be written as a fraction or a ratio of two integers. Signup and view all the answers

What are real numbers?

The set of all rational numbers is also called this. Signup and view all the answers

Define set-builder notation.

Mathematical notation used to show the answer to an inequality. Signup and view all the answers

What is the solution in mathematical terms?

A quantity which makes a statement true. Signup and view all the answers

What does 'union' refer to in compound inequalities?

The graph of a compound inequality containing the word 'or'. Signup and view all the answers

What is a variable in mathematics?

A symbol, usually a letter, used to represent an unknown quantity. Signup and view all the answers

Define whole numbers.

The set of natural numbers as well as the number zero. Signup and view all the answers

Study Notes

Equations and Inequalities Vocabulary

Absolute Value: Refers to the distance of a number from zero on the number line, denoted as |x|.
Algebraic Expressions: These expressions include variables, constants, and arithmetic operations, forming mathematical phrases like 2x + 3.
Compound Inequality: Involves two separate inequalities combined, often linked by 'and' or 'or', graphed together on a coordinate plane.
Empty Set: The solution set for an equation with no real solutions, often represented by the symbol ∅ or {}.
Equation: A mathematical statement asserting the equality of two expressions, such as -5x² = -125.
Formula: A concise way to express the relationship between variables, like A = πr² for the area of a circle.
Integers: Consist of whole numbers that can be positive, negative, or zero without fractional or decimal parts.
Intersection: The overlap of graphs in a compound inequality expressed with 'and', representing common solutions.
Irrational Numbers: Include numbers that cannot be expressed as fractions or ratios, like π and √2, extending infinitely without repeating.
Natural Numbers: The set of positive counting numbers starting from 1 and does not include zero.
Open Sentence: A mathematical sentence involving variables, leaving room for solutions (e.g., x + 3 = 5).
Order of Operations: The specific rules that dictate the sequence in which operations should be performed in expressions, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Rational Numbers: Numbers expressible as a fraction a/b, where a and b are integers and b ≠ 0, encompassing whole numbers and terminating or repeating decimals.
Real Numbers: The complete set of rational and irrational numbers, each corresponding to a point on the number line.
Set-Builder Notation: A shorthand for describing a set by stating the properties that its members must satisfy, commonly used for inequalities.
Solution: A specific value or set of values that satisfy an equation or inequality, making it true.
Union: The combination of two sets or graphs from a compound inequality connected with 'or', including all solutions from both inequalities.
Variable: Typically represented by letters, these symbols denote unknown quantities in equations and expressions, such as x, y, or z.
Whole Numbers: Comprise the set of natural numbers plus zero, including {0, 1, 2, 3,...}.

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Test your knowledge of key vocabulary terms related to equations and inequalities in Algebra. This quiz covers fundamental concepts such as absolute value, algebraic expressions, compound inequalities, and empty sets. Perfect for anyone studying Algebra Chapter 1.