Algebra Chapter 1: Equations and Inequalities Vocabulary

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,...}.