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Linear Inequalities in One Variable definitions

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  • Linear Inequality
    An expression involving an inequality symbol between linear terms, representing a range of possible values for a variable.
  • Inequality Symbol
    A sign such as >, <, ≥, or ≤ used to compare values and indicate the relationship between expressions.
  • Solution Set
    A collection of all values that satisfy a linear inequality, often shown as a range rather than a single value.
  • Set Builder Notation
    A format using curly brackets and a vertical line to describe all values meeting a specific inequality condition.
  • Interval Notation
    A concise way to express ranges of solutions using parentheses or brackets to indicate inclusion or exclusion of endpoints.
  • Number Line
    A visual representation of solution sets, using arrows, dots, or brackets to show included or excluded values.
  • Parenthesis
    A symbol used in interval notation or graphs to indicate that a boundary value is not included in the solution set.
  • Square Bracket
    A symbol used in interval notation or graphs to show that a boundary value is included in the solution set.
  • Open Circle
    A graphical marker on a number line indicating a value is excluded from the solution set.
  • Closed Circle
    A graphical marker on a number line indicating a value is included in the solution set.
  • Addition Property of Inequality
    A rule allowing the same value to be added to both sides of an inequality without changing the solution set.
  • Subtraction Property of Inequality
    A rule allowing the same value to be subtracted from both sides of an inequality without affecting the solution set.
  • Multiplication Property of Inequality
    A rule permitting multiplication of both sides by a positive value, preserving the direction of the inequality.
  • Division Property of Inequality
    A rule permitting division of both sides by a positive value, maintaining the direction of the inequality.
  • Symbol Flipping
    A required change in the direction of the inequality sign when multiplying or dividing both sides by a negative value.