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Solving Linear Inequalities definitions

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  • Linear Inequality
    An algebraic statement using an inequality symbol instead of an equal sign, representing a range of possible solutions.
  • Inequality Symbol
    A sign such as >, <, ≥, or ≤ used to compare two expressions, indicating their relative size or order.
  • Solution Set
    All values that make an inequality true, often represented as a range rather than a single number.
  • Set Builder Notation
    A method using curly brackets and a vertical line to describe all values satisfying a given condition.
  • Interval Notation
    A concise way to express all numbers between two endpoints, using parentheses or brackets to show inclusion or exclusion.
  • Number Line
    A visual representation where solutions are shown as arrows, brackets, or circles to indicate included or excluded values.
  • Parenthesis
    A symbol used in interval notation or graphs to show that a boundary value is not included in the solution.
  • Bracket
    A symbol used in interval notation or graphs to indicate that a boundary value is included in the solution.
  • Open Circle
    A notation on a graph showing that a specific value is not part of the solution set.
  • Closed Circle
    A notation on a graph indicating that a specific value is included in the solution set.
  • Three Part Inequality
    An inequality with a variable expression between two inequality symbols, representing values between two bounds.
  • Variable Isolation
    The process of rearranging an inequality to get the variable alone on one side or in the center.
  • Addition Property of Inequality
    A rule stating that adding the same value to each side of an inequality keeps the relationship true.
  • Multiplication Property of Inequality
    A rule stating that multiplying each side of an inequality by a positive value keeps the relationship true, but by a negative value reverses the symbol.
  • Coefficient
    A numerical factor multiplying a variable in an algebraic expression, affecting the solution when isolating the variable.