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Absolute Value Inequalities definitions

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  • Absolute Value
    Represents the distance from zero, always non-negative, and is used to express how far a number is from zero on the number line.
  • Inequality
    A mathematical statement comparing two expressions, indicating if one is less than, greater than, or equal to the other.
  • Three-Part Inequality
    A compound statement showing a variable between two values, used for solutions where absolute value is less than a number.
  • Interval Notation
    A concise way to represent solution sets using brackets or parentheses to show inclusion or exclusion of endpoints.
  • Bracket
    A symbol in interval notation or graphs indicating that an endpoint is included in the solution set.
  • Parenthesis
    A symbol in interval notation or graphs indicating that an endpoint is not included in the solution set.
  • Closed Circle
    A graphical marker used to show that a specific value is included in the solution set.
  • Open Circle
    A graphical marker used to show that a specific value is not included in the solution set.
  • Compound Inequality
    A statement combining two inequalities, often joined by 'or', representing multiple solution intervals.
  • Solution Set
    The collection of all values that satisfy a given inequality or equation.
  • Special Case
    A scenario where the value compared to absolute value is zero or negative, leading to unique solution outcomes.
  • All Real Numbers
    A solution set including every possible value on the number line, often resulting from certain absolute value inequalities.
  • No Solution
    A situation where no values satisfy the given inequality, often occurring when absolute value is less than a negative.
  • Distance
    A measure of how far a value is from zero, fundamental to understanding absolute value expressions.
  • Variable
    A symbol representing an unknown value, typically placed at the center of inequalities to be solved.