Linear inequality solver
Choose the inequality sign and enter the coefficients to get the solution set written two ways.
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How to use it
- Enter coefficient a, constant b, sign and right side c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
ax + b < c becomes ax < c - b, then divide by a. If a is negative the inequality sign flips. If a = 0 the answer is all real numbers or no solution.
Example
Inputs: Coefficient a = -3, Constant b = 2, Sign = greater than or equal (≥), Right side c = 8. Result: Solution: x ≤ -2.
Limits and caveats
- One-variable linear inequalities only.
- If x appears on both sides, move it to the left side before entering.
Questions about this tool
Why does the sign flip when dividing by a negative?
Multiplying by a negative reverses order: 2 < 3 but -2 > -3.
What is the difference between ( and [?
A square bracket means the endpoint is included (≤ or ≥); a round bracket means it is not (< or >).
How do I solve 5 - 2x > 1?
Write it as -2x + 5 > 1, so a = -2, b = 5, c = 1. The answer is x < 2.