Inequality Solver Calculator

Work out inequality solver instantly with clear inputs, formula shown and shareable results.

About Inequality Solver Calculator

Solving a linear inequality follows the same steps as an equation, with one crucial difference: multiplying or dividing by a negative number reverses the direction of the inequality.

Formula

Linear inequality

ax + b < c ⇒ x < (c − b)/a if a > 0, and x > (c − b)/a if a < 0

Worked example

With the default values below, Inequality Solver Calculator returns Solution of x > -3. Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient a in ax + b ? c: -2
Constant b: 5
Right-hand side c: 11
Relationone of <, ≤, >, ≥: <

Results

Solution: x > -3
Boundary value: -3.00000000
Interval notation: (-3, ∞)
Inequality reversed: Yes, dividing by a negative reversed the inequality

Step by step

1Values used
2Linear inequality
3Solution= x > -3
4Boundary value= -3.00000000
5Interval notation= (-3, ∞)
6Inequality reversed= Yes, dividing by a negative reversed the inequality

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Solve −2x + 5 < 11.

−2x < 6, and dividing by −2 flips the sign to give x > −3.

Why does the direction flip?

Multiplying by a negative reflects the number line, so the order of any two values is reversed.