Primary formula
Move terms to one side, find critical points, and test signs across intervals.
Math calculator
Inequality Calculator
Solve linear, quadratic, compound and absolute-value inequalities with interval notation and number-line context.
Last reviewed: July 4, 2026Math algebra and geometry engine v1.0.0
Math calculator
Inequality Calculator
Calculations run locally from the values entered. Exact values and decimal approximations are labelled separately.
Exact math engine
Mode
Solve a linear or quadratic polynomial inequality.
Enter values and choose Calculate to show the result below the calculator.
Formula and assumptions
Input assumptions
Inputs represent ideal mathematical objects. Only supported modes, units and expression forms are calculated. Rounded values are display approximations unless an exact result is labelled.
Precision note
Exact rational algebra is labelled. Results involving pi, radicals, trigonometry, geometry approximations or rounded unit conversions are shown as decimal approximations where appropriate.
Algebra, geometry and measurement flow
Parse
Read equations, polynomials, inequalities, dimensions, units, shapes or coordinates from labelled fields.
Validate
Apply expression, system-size, inequality, unit-dimension, shape and coordinate checks before calculating.
Calculate
Use deterministic TypeScript, exact rational arithmetic and bounded decimal methods where appropriate.
Label
Separate exact values, approximations, diagrams, tables, exports and warnings.
What is the Inequality Calculator?
Inequality Calculator is a local NexaCalc math tool for one-variable inequality solving and interval notation. It keeps the entered assumptions visible, separates exact and approximate output, and avoids arbitrary expression execution.
The page is intended for educational checking, planning and transparent formula work. It is not a substitute for independent review in academic, engineering or professional settings.
How to use the Inequality Calculator
Choose the calculation mode, enter labelled values, select units where shown, then use Calculate. Reset restores the built-in example so the page can be tested quickly.
When a result depends on a convention, the calculator labels that convention in the result, step list and formula area.
Formula and method
The parser reduces supported expressions to polynomial sign tests. Linear, quadratic, compound and absolute-value modes use bounded interval logic.
Worked example
x^2 - 5x + 6 >= 0 gives (-infinity, 2] union [3, infinity).
Exact and approximate results
Rational algebra is kept exact where practical. Values involving pi, square roots, trigonometric functions or approximation formulas are labelled as decimal approximations unless an exact symbolic form is also shown.
Limitations
The calculator intentionally supports a bounded set of common school and practical math cases so it remains fast, deterministic and safe in the browser.
- Guaranteed symbolic solving is limited to degree 2.
- Rational inequalities are not the primary mode.
- Multivariable inequalities are rejected.
Privacy and performance
Inputs are calculated in the browser session. NexaCalc does not upload equations, dimensions or coordinates to a third-party math service for these tools.
Frequently asked questions
Does the Inequality Calculator use eval or arbitrary code execution?
No. Supported expressions are parsed by a limited deterministic parser and unsupported tokens are rejected.
Are exact and rounded answers different?
Yes. Exact answers preserve rational values or symbolic pi where practical. Decimal approximations are rounded display values.
Why are there input limits?
Limits keep the tool responsive on shared hosting and prevent unbounded loops, oversized expressions or very large tables.
Can I use the result for professional work?
Use it as an educational check. Verify important academic, engineering, construction or professional work independently.
References
- OpenStax College Algebra 2e, Polynomial and Rational Functions, Jay Abramson, OpenStax. Source.
- OpenStax College Algebra 2e, Systems of Equations and Inequalities, Jay Abramson, OpenStax. Source.
- OpenStax Prealgebra 2e, Geometry applications, Marecek, Anthony-Smith and Mathis, OpenStax. Source.
- OpenStax College Algebra 2e, Rates of Change and Behavior of Graphs, Jay Abramson, OpenStax. Source.
Reference set reviewed July 4, 2026.
Educational disclaimer
This calculator provides mathematical results from the values, conventions and methods you enter. Verify important academic, engineering or professional work independently.