Online Tool Store
Inequality Solver
Solve linear inequalities step by step and view the result as algebraic notation, interval notation, and set-builder notation alongside a plotted number line.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Solution Inequality
Algebraic variable form
Interval Notation
Standard mathematical interval
Set-Builder Notation
{ x ∈ ℝ | condition }
Visual Number Line Graph
How it works
- Enter your linear inequality coefficients (a, inequality sign, and constant b).
- The solver applies algebraic rules, automatically reversing the inequality operator if divided by a negative coefficient.
- View the solution in algebraic notation, standard interval notation, and set-builder notation.
- Examine the rendered SVG number line graph featuring proper boundary shading and open/closed endpoint markers.
FAQ
Why does the inequality sign flip when multiplying or dividing by a negative number?
Multiplying or dividing both sides of an inequality by a negative value reverses their relative order on the number line (for example, while 2 < 5, multiplying by -1 yields -2 > -5).
What is the difference between open and closed interval brackets?
A square bracket [ or ] indicates that the endpoint value is included in the solution set (strict inequality with ≤ or ≥). A round parenthesis ( or ) indicates that the endpoint is excluded (< or >). Infinity (±∞) is always enclosed with a round parenthesis.
What is set-builder notation?
Set-builder notation is a mathematical shorthand describing a set of numbers by specifying the condition that members must satisfy, formatted as { x ∈ ℝ | x ≤ 4 } (read as "the set of all real numbers x such that x is less than or equal to 4").
How is an open circle vs closed circle represented on a number line?
A filled/solid circle indicates a closed inclusive boundary (≤ or ≥), whereas a hollow/open circle indicates an open strict boundary (< or >).
How we compare
| Feature | Online Tool Store | Symbolic algebra engines | Graphing calculators |
|---|---|---|---|
| Instant vector SVG number line plot | ✓ | ✗ (Text only) | ✓ |
| Simultaneous Interval & Set-Builder formats | ✓ | ✓ | ✗ |
| Automatic negative sign flipping logic | ✓ | ✓ | ✓ |