Math Algebra • Inequalities
Shaded region satisfies the chosen logical combination. Dashed lines are strict inequalities. Axis ticks and intercepts are labeled.
Each row’s \(y=f_i(x)\) (solid) with its reference line \(y=k_i\) (dashed). Crossing points \(f_i(x)=k_i\) are marked and labeled.
Number line: green segments show the solution; closed/open endpoints reflect ≤/≥ vs </> (endpoints labeled).
AND means the solution must satisfy all included conditions at the same time, which corresponds to an intersection of solution sets. OR means the solution can satisfy at least one condition, which corresponds to a union of solution sets.
NOT takes the complement of a row’s solution set, meaning values that do not satisfy that inequality. In 1D this is the complement in the real line, and in 2D it is the complement in the plane.
Use row numbers like 1, 2, 3 to refer to the listed inequalities and combine them with AND/OR/NOT (or ∧, ∨, ¬) and parentheses. For example, 1 AND (2 OR NOT 3) applies the operations to the sets produced by those rows.
A 2D linear inequality defines a half-plane in the x-y plane, so the combined solution becomes a region rather than an interval on a number line. When any 2D row is present, the calculator visualizes the combined feasible region with shading.
Endpoints are closed when the inequality includes equality (≤ or ≥) and open when it is strict (< or >). The number line display reflects this by showing filled or open endpoints.