Last updated October 4, 2026 · Report an error
Graphing a linear inequality on a number line always comes down to two decisions: where the boundary point goes, and whether the circle there is open or closed. This tool solves the inequality and spells out exactly how to draw it.
How it works
The inequality ax+b {op} 0 is solved for x (flipping the inequality direction if a is negative), then described as an open circle (for < or >) or closed circle (for ≤ or ≥) at the boundary, shaded in the direction the inequality points.
- Enter a (coefficient of x).
- Enter b (constant).
- Enter inequality.
- Click Calculate to see your results.
Examples
A strict inequality
x-5 < 0 solves to x < 5: an open circle at 5, shading to the left.
An inclusive inequality with a negative coefficient
-2x+4 ≤ 0 solves to x ≥ 2 (the inequality flips): a closed circle at 2, shading to the right.
Who should use it
- Algebra coursework on graphing linear inequalities.
- Double-checking a hand-drawn number line graph.
Industry applications
- Mathematics education
Advantages
- Automatically handles the sign-flip rule for negative coefficients.
- Gives interval notation alongside the plain-English description.
Limitations
- Only describes the graph in words — doesn't render an actual image of the number line.
Common mistakes to avoid
- Forgetting to flip the inequality sign when dividing by a negative coefficient.
Best practices
- Test a point from your shaded region back in the original inequality — it should make the inequality true.
Tips
- A quick memory trick: "less than" points left, "greater than" points right — matching the direction the inequality symbol itself "opens" toward.
Frequently asked questions
A closed (filled-in) circle means the boundary value itself is included in the solution (≤ or ≥), while an open circle means it's excluded (< or >).
Dividing (or multiplying) both sides of an inequality by a negative number reverses its direction — this tool applies that rule automatically whenever the x-coefficient is negative.