Graph any inequality on a number line instantly — see open and closed circles, shaded intervals, and interval notation all in one place. Free, no sign-up required.
Why this page is built for number line intent
Number Line Grapher
Built to graph inequalities on a number line with open/closed endpoint detection, shaded interval display, and interval notation output.
Supported Input Styles
Quick rules
Strict signs, excluded boundary, parentheses in interval notation.
Inclusive signs, included boundary, brackets in interval notation.
You can also type forms like (2, inf) or (-inf, 2] U [5, inf).
Math Keyboard
Tap brackets, infinity, unions, and inequality signs for fast interval-notation input.
Result
Open circle at x = 2 with shading to the right.
Graph
Number Line
Drag to pan. Use the controls or mouse wheel to zoom the view.
Interval
(2, +∞)
Solution
x > 2
Endpoint rule
Open circle at x = 2 with shading to the right.
How to read this graph
Open circle at x = 2 — the boundary value is not included.
Shading extends to the right — all values greater than 2 satisfy the inequality.
Check a value on the number line
Recent History
Saved locally in this browser so you can return to recent number-line graphs without any backend.
Zone 3
Use this chart when you want to check the visual pattern of an inequality fast. The inequality form, endpoint rule, number-line shape, and interval notation should all agree.
| Inequality | Number Line Shape | Endpoint | Interval | Try it |
|---|---|---|---|---|
| x > a | ○══════→ | Open at a | (a, +∞) | |
| x ≥ a | ●══════→ | Closed at a | [a, +∞) | |
| x < a | ←══════○ | Open at a | (-∞, a) | |
| x ≤ a | ←══════● | Closed at a | (-∞, a] | |
| a < x < b | ○══════○ | Open at both | (a, b) | |
| a ≤ x ≤ b | ●══════● | Closed at both | [a, b] | |
| a < x ≤ b | ○══════● | Open left, closed right | (a, b] | |
| a ≤ x < b | ●══════○ | Closed left, open right | [a, b) | |
| x < a or x > b | ←══○ ○══→ | Open at both | (-∞, a) ∪ (b, +∞) | |
| x ≤ a or x ≥ b | ←══● ●══→ | Closed at both | (-∞, a] ∪ [b, +∞) |
Calculator Types
Solve one-variable linear inequalities with steps, interval notation, and a clean number-line graph.
Graph any inequality on a number line with open and closed endpoint detection, shading direction, and interval notation output.
Solve quadratic inequalities with sign analysis, roots, interval notation, and a number-line graph.
Solve absolute value inequalities with case splitting, interval notation, and step-by-step explanations.
Solve compound inequalities with interval intersection, union logic, and graph output.
Solve rational inequalities with steps, excluded values, sign charts, and interval notation.
Zone 4
The fastest way to use this calculator is to type the inequality exactly as you would write it — x > 2, x <= -1, -3 < x <= 5, or x < -2 or x >= 4. If the inequality is already solved, the page goes straight to graphing. If the inequality still has a variable expression such as 2x + 3 > 7, the page solves it first and then graphs the result.
The number line is the main output on this page, not a secondary tab. The graph appears immediately after you enter the inequality, and the endpoint markers — open circles for strict symbols and closed circles for inclusive symbols — are labeled so the difference between > and ≥ is visible at a glance. The shading direction and the interval notation update together, so you can always check that the graph and the notation are telling the same story.
The Number Line Quick Reference chart below the calculator is useful when you want to check the pattern for a specific inequality type without entering a new problem. Each row shows the inequality form, the number line shape, the endpoint rule, and the interval notation together. Click any Load example button to see that pattern in the calculator.
If you want the dedicated notation converter, open the interval notation calculator. For chained or union-style logic, move next to the compound inequality calculator.
Enter an inequality such as x > 2, -3 < x ≤ 5, or x < -2 or x ≥ 4.
Read the number line graph: check the endpoint type (open or closed circle) and the shading direction.
Use the Interval Notation and All Notations tabs to confirm the same answer in symbolic form.
A number line graph of an inequality shows every value that satisfies the inequality as a shaded region. The boundary value — the number the variable is being compared to — is marked with a circle. An open circle means the boundary is not included in the solution. A closed circle means the boundary is included.
The shading extends in one direction from the boundary, or between two boundaries, depending on the inequality. For x > 2, the shading goes right from 2 because all numbers greater than 2 satisfy the inequality. For x ≤ -1, the shading goes left from -1 because all numbers less than or equal to -1 satisfy it. For a compound inequality like -3 < x ≤ 5, the shading is bounded — it fills the space between the two boundary values.
The open and closed circle distinction is the most important visual detail on the number line. It corresponds directly to the difference between strict symbols (> and <, which use parentheses in interval notation) and inclusive symbols (≥ and ≤, which use brackets). Getting the circle type right is not a cosmetic choice — it changes the actual solution set.
| Feature | Open circle ○ | Closed circle ● |
|---|---|---|
| Inequality symbol | > or < (strict) | ≥ or ≤ (inclusive) |
| Boundary included? | No | Yes |
| Interval notation | Parenthesis ( or ) | Bracket [ or ] |
| Example | x > 2 → ○ at 2 | x ≥ 2 → ● at 2 |
Graphing an inequality on a number line takes three decisions: find the boundary value, choose the circle type, and choose the shading direction. Once those three decisions are made, the graph draws itself. For a longer lesson view, see how to graph inequalities on a number line.
The boundary value is the number on the right side of a solved inequality. For x > 2, the boundary is 2. For x ≤ -4, the boundary is -4. If the inequality is not yet solved — for example 2x + 3 > 7 — solve it first to find the boundary.
Use an open circle if the symbol is strict (> or <). The boundary value is not part of the solution. Use a closed circle if the symbol is inclusive (≥ or ≤). The boundary value is part of the solution.
Greater than (> or ≥): shade to the right of the boundary. Less than (< or ≤): shade to the left of the boundary. Compound AND inequality (a < x < b): shade between the two boundaries. Compound OR inequality (x < a or x > b): shade two separate rays, one on each side.
The circle type and shading direction translate directly into interval notation. An open circle becomes a parenthesis. A closed circle becomes a bracket. Shading to the right with no upper bound ends with +∞). Shading to the left with no lower bound starts with (-∞.
Example graph rule
Notation check
Open circles become parentheses. Closed circles become brackets. This is the same rule used in interval notation.
An open circle means the boundary value is not included in the solution — it corresponds to a strict inequality symbol (> or <). A closed circle means the boundary value is included — it corresponds to an inclusive symbol (≥ or ≤).
Shade to the right. Greater than means values larger than a, which are to the right of a on the number line.
Place an open circle at -3 and a closed circle at 5, then shade the region between them. The open circle reflects the strict < symbol and the closed circle reflects the inclusive ≤ symbol.
Graph two separate shaded regions — one ray going left from -2 (open circle) and one ray going right from 4 (closed circle). These are two disjoint intervals on the same number line.
Yes. The calculator solves the inequality first and then graphs the result. You will see both the solving steps and the final number line graph.
They represent the same solution set in different forms. An open circle corresponds to a parenthesis, a closed circle corresponds to a bracket, a rightward ray corresponds to +∞, and a leftward ray corresponds to -∞.
Zone 6
Keep the visual rules close by while you compare open circles, brackets, compound graphs, and interval notation.