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Math

Linear Inequality Calculator

Solve ax + b < c, ≤ c, > c or ≥ c and reverse the inequality correctly for a negative coefficient.

Exact method explained belowEditable inputs
Calculation notebook
Calculation notebook

The formula and worked example below explain the calculation.

See the method

Enter your values

Runs on your device

Your answer

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter coefficient a, constant b, relation, right side c.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Move b to the right. Divide by a, reversing the comparison when a is negative. If a is zero, evaluate the constant comparison directly.

A WORKED EXAMPLE

Using coefficient a = -2, constant b = 3, relation = lt, right side c = 9, the result is x > -3. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Dividing by a negative number reverses order on the real line. The calculator applies that rule before displaying the solution boundary.

What to keep in mind

Solves one linear inequality, not chained inequalities or expressions with variable denominators. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.

Common questions

Why can the inequality sign change?

Dividing by a negative number reverses order on the real line. The calculator applies that rule before displaying the solution boundary.

How can I check the result?

Move b to the right. Divide by a, reversing the comparison when a is negative. If a is zero, evaluate the constant comparison directly. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.

Methodology maintained by ClarityKit. How these tools are built and checked.