Graphing Inequalities on a Number Line Calculator
Enter a linear inequality ax + b op c, pick the operator (>, ≥, <, ≤), and instantly see the solved form, boundary point, interval notation, and the solution graphed on a number line.
Inequality operator
- 1
Move constant to right side
3 − 0 = 3 - 2
Divide by coefficient a
3 ÷ 1 = 3
How does this calculator work?
To solve ax + b op c: subtract b from both sides, then divide by a — but flip the inequality symbol if a is negative. The boundary is (c − b) / a. An open endpoint (strict >, <) excludes the boundary; a closed endpoint (≥, ≤) includes it. Interval notation uses parentheses for open and brackets for closed ends.
Formula
How this is calculated
A linear inequality in one variable has the form ax + b op c, where op is one of >, ≥, <, or ≤. To solve, the constant b is moved to the right side (giving ax op c − b) and then both sides are divided by a to isolate x. The critical rule is that dividing (or multiplying) by a negative number reverses the direction of the inequality, so when a < 0 the operator is flipped automatically.
The solution is a ray on the number line starting at the boundary value (c − b) / a. An open endpoint (○) means the boundary itself is excluded (strict inequalities > and <), while a closed endpoint (●) means it is included (≥ and ≤). The solution in interval notation uses parentheses for open ends and square brackets for closed ends, with +∞ or −∞ always open.
Assumptions: the coefficient a must be non-zero (otherwise the equation is not linear in x and may have no solution or all reals as solution). The computation uses standard floating-point arithmetic; boundary values are shown to 4–6 decimal places.
Frequently asked questions
Dividing both sides of an inequality by a negative number reverses the relationship between them: for example, 4 > 2 but −4 < −2. The same rule applies when dividing the inequality ax op c − b by the coefficient a whenever a is negative.
A closed endpoint (solid circle ●) means the boundary value satisfies the inequality, so it is part of the solution set (used with ≥ or ≤). An open endpoint (hollow circle ○) means the boundary value is not included (used with strict > or <).
A compound inequality defines a bounded interval. Split it into two simple inequalities (x > 2 and x ≤ 5), solve each with this calculator, and then take the overlap. The result is the interval (2, 5], a segment with an open left end and a closed right end.
Also known as
TG we-Calculate Editorial Team. (2026). Graphing Inequalities on a Number Line Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/graphing-inequalities-1d-calculator
TG we-Calculate Editorial Team. "Graphing Inequalities on a Number Line Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/graphing-inequalities-1d-calculator.
TG we-Calculate Editorial Team, "Graphing Inequalities on a Number Line Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/graphing-inequalities-1d-calculator
@misc{wecalculate_graphing_inequalities_1d_calculator, title = {Graphing Inequalities on a Number Line Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/graphing-inequalities-1d-calculator}}, year = {2026}, note = {TG we-Calculate} }
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