Compound Inequality Calculator

Q: Solve 1 < 3x − 2 < 13.

Add 2 to get 3 < 3x < 15, then divide by 3 to get 1 < x < 5.

Q: What if a is negative?

Both comparisons flip, so the endpoints swap places; the calculator orders them for you.

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

About Compound Inequality Calculator

A compound inequality is solved by applying the same operation to all three parts at once. If the coefficient is negative both inequalities reverse, which swaps which endpoint is the lower one.

Formula

Compound inequality

p < ax + b < q ⇒ (p − b)/a and (q − b)/a are the endpoints, ordered by the sign of a

Worked example

With the default values below, Compound Inequality Calculator returns Solution interval of 1 < x < 5. Change any input above and every figure here is recalculated in your browser.

Inputs used

Lower bound: 1
Coefficient a in lower < ax + b < upper: 3
Constant b: -2
Upper bound: 13

Results

Solution interval: 1 < x < 5
Lower limit for x: 1.00000000
Upper limit for x: 5.00000000
Width of the interval: 4.00000000

Step by step

1Values used
2Compound inequality
3Solution interval= 1 < x < 5
4Lower limit for x= 1.00000000
5Upper limit for x= 5.00000000
6Width of the interval= 4.00000000

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 1 < 3x − 2 < 13.