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Linear Inequalities definitions

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  • Interval Notation
    A compact way to represent solution sets using parentheses and square brackets to indicate inclusion or exclusion of endpoints.
  • Closed Interval
    A set of numbers including its endpoints, denoted with square brackets and represented by closed circles on a number line.
  • Open Interval
    A set of numbers excluding its endpoints, denoted with parentheses and represented by open circles on a number line.
  • Half-Open Interval
    A set where one endpoint is included and the other is excluded, shown with a mix of square bracket and parenthesis.
  • Inequality Symbol
    A mathematical sign such as <, >, ≤, or ≥ used to compare values and define solution ranges.
  • Linear Inequality
    An algebraic statement similar to a linear equation but using an inequality symbol instead of an equals sign.
  • Endpoint
    A boundary value in an interval, which may be included or excluded from the solution set.
  • Number Line
    A visual representation used to graphically display intervals and solution sets for inequalities.
  • Closed Circle
    A filled dot on a number line indicating that the corresponding endpoint is included in the interval.
  • Open Circle
    A hollow dot on a number line indicating that the corresponding endpoint is excluded from the interval.
  • Infinity Symbol
    A notation used in interval notation to represent unbounded intervals extending indefinitely in one direction.
  • Least Common Denominator
    The smallest shared multiple of denominators used to eliminate fractions when solving inequalities.
  • Solution Set
    All possible values that satisfy a given inequality, often expressed in interval notation.
  • Algebraic Manipulation
    The process of rearranging and simplifying expressions to isolate variables and solve inequalities.
  • Flipping the Inequality
    The required reversal of the inequality symbol when both sides are multiplied or divided by a negative number.