Algebraic Inequations Study Cards

Enhance Your Learning with Algebraic Inequations Flash Cards for quick learning



Inequation

A mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥).

Linear Inequation

An inequation where the highest power of the variable is 1.

Quadratic Inequation

An inequation where the highest power of the variable is 2.

Rational Inequation

An inequation where the variable appears in the denominator of a rational expression.

Absolute Value Inequation

An inequation involving the absolute value of a variable.

Exponential Inequation

An inequation where the variable appears as an exponent.

Logarithmic Inequation

An inequation where the variable appears inside a logarithm.

Trigonometric Inequation

An inequation involving trigonometric functions of the variable.

Polynomial Inequation

An inequation where the variable appears in a polynomial expression.

Radical Inequation

An inequation where the variable appears inside a radical.

System of Inequations

A set of two or more inequations with the same variables.

Intersection

The solution set of a system of inequations where all the individual inequations are satisfied simultaneously.

Union

The solution set of a system of inequations where at least one of the individual inequations is satisfied.

Infinite Solutions

The solution set of a system of inequations where any value of the variable satisfies all the individual inequations.

No Solution

The solution set of a system of inequations where there is no value of the variable that satisfies all the individual inequations.

Interval Notation

A way to represent the solution set of an inequation using intervals on the number line.

Open Interval

An interval that does not include its endpoints.

Closed Interval

An interval that includes its endpoints.

Half-Open Interval

An interval that includes one endpoint but not the other.

Infinite Interval

An interval that extends indefinitely in one or both directions.

Solution Set

The set of all values of the variable that satisfy an inequation.

Inequality Symbol

A symbol used to compare two expressions in an inequation.

Less Than

The inequality symbol (<) used to indicate that one expression is smaller than another.

Greater Than

The inequality symbol (>) used to indicate that one expression is larger than another.

Less Than or Equal To

The inequality symbol (≤) used to indicate that one expression is smaller than or equal to another.

Greater Than or Equal To

The inequality symbol (≥) used to indicate that one expression is larger than or equal to another.

Compound Inequation

An inequation that combines two or more individual inequations using the logical operators 'and' or 'or'.

And

The logical operator used to combine two individual inequations in a compound inequation, indicating that both inequations must be satisfied.

Or

The logical operator used to combine two individual inequations in a compound inequation, indicating that at least one of the inequations must be satisfied.

Intersection of Solution Sets

The set of values that satisfy both individual inequations in a compound inequation.

Union of Solution Sets

The set of values that satisfy at least one of the individual inequations in a compound inequation.

Infinite Solutions for a Compound Inequation

The compound inequation has an infinite number of values that satisfy it.

No Solution for a Compound Inequation

The compound inequation has no values that satisfy it.

Graphing Inequations

Representing the solution set of an inequation on a coordinate plane.

Boundary Line

The line that separates the solution region from the non-solution region in a graphed inequation.

Shaded Region

The region on the coordinate plane that represents the solution set of a graphed inequation.

Solid Line

A line used to represent the boundary of an inequation when the inequality symbol includes 'or equal to' (≤ or ≥).

Dashed Line

A line used to represent the boundary of an inequation when the inequality symbol does not include 'or equal to' (< or >).

Positive Solution

A value of the variable that makes the inequation true.

Negative Solution

A value of the variable that makes the inequation false.

No Solution for a Graphed Inequation

The graphed inequation does not have any points that satisfy it.

Infinite Solutions for a Graphed Inequation

The graphed inequation has an infinite number of points that satisfy it.

Real-Life Applications of Inequations

Applying inequations to solve real-world problems involving constraints, inequalities, and optimization.

Optimization

Finding the maximum or minimum value of a quantity within given constraints.

Feasible Region

The set of all possible solutions to a system of inequations in an optimization problem.

Objective Function

The quantity to be optimized in an optimization problem.

Corner Point

A point in the feasible region of an optimization problem where the objective function reaches its maximum or minimum value.

Infeasible Region

The set of values that do not satisfy the constraints in an optimization problem.

Unbounded Region

The set of values that satisfy the constraints in an optimization problem, but the objective function does not have a maximum or minimum value.