Graphing inequalities on a number line is the first step to understanding solution sets. A filled circle means the endpoint is included, an open circle means it is not, and the shaded part shows every number that satisfies the condition.
How to use the Graphing Inequalities on a Number Line Calculator
- Number of inequalities
- Combine with
- Inequality 1: x is
- Value 1
- Inequality 2: x is
- Value 2
- Inequality 3: x is
- Value 3
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How it works
With “and” the calculator intersects the conditions (all must be true); with “or” it takes their union (at least one is true). The bold segment of the number line shows the solution.
Formula
x < a → (−∞, a) x ≤ a → (−∞, a] x > a → (a, ∞) x ≥ a → [a, ∞)
Worked example
Inputs — Number of inequalities: 2; Combine with: and (all must hold); Inequality 1: x is: ≥ (greater than or equal to); Value 1: -1; Inequality 2: x is: < (less than); Value 2: 3.
Results — Solution (interval notation) = [−1, 3); Inequalities = x ≥ −1 and x < 3; Number line = ──────────●━━━━━━━━━━━━━━━━━━━○──────────
−3 5.
Key terms
- Number line
- A line on which every point represents a real number.
Frequently asked questions
What does a closed dot mean?
The endpoint is included (≤ or ≥).
What does an open dot mean?
The endpoint is excluded (< or >).
What is the difference between "and" and "or"?
"And" keeps only the overlap; "or" keeps everything covered by at least one inequality.
Can a compound inequality have no solution?
Yes, for example x < 1 and x > 3.