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Inequality Solver

Tool/Math solver to resolve inequalities. An inequation is a mathematical expression presented as an inequality between two elements with unknown variables.

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Inequality Solver - dCode

Tag(s) : Symbolic Computation

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- Mathematics
- Symbolic Computation
- Inequality Solver

## Inequality solving

## Answers to Questions (FAQ)

### What is an inequality? (Definition)

An inequality is a mathematical comparison between 2 elements separated by a comparator operator (greater, less, different) and each of the sides that can contain variables/unknowns.

### How to solve an inequality?

Enter the inequality or inequalities to be solved, and the unknown variables to be found.

__Example:__ $ x+2 > 0 $ has for solution $ x > -2 $

Inequalities can be combined, either by writing one inequality per line, either with the and (logical conjunction) operator: `&&` or `⋀`.

__Example:__ $ 2x+1 >= 0 \ \&\& \ 3x-1 >= 0 $

Solutions are presented with logical simplifications (not in interval notation form).

Be sure to correctly indicate the solving domain set, if the expected result is an integer, indicate the natural integers number set otherwise prefer the real numbers set R. Use the complex domain C only if the solution is a complex number.

### What are calculation techniques for solving inequalities?

Inequality solving is similar to equation solving, however, the presence of the comparison sign involves a few additional rules:

— Multiplying by the same strictly negative real number on each side of an inequality changes the direction of the inequality: if $ a < b $ and $ c < 0 $ then $ a \times c > b \times c $

— Multiplying by the same strictly positive real number on each side of an inequality does not change the direction of the inequality: if $ a < b $ and $ c > 0 $ then $ a \times c < b \times c $

— Dividing by the same strictly negative real number on each side of an inequality changes the direction of the inequality: if $ a < b $ and $ c < 0 $ then $ \frac{a}{c} > \frac{b}{c} $

— Dividing by the same strictly positive real number on each side of an inequality does not change the direction of the inequality: if $ a < b $ and $ c > 0 $ then $ \frac{a}{c} < \frac{b}{c} $

— Adding the same real number (positive or negative) on each side of an inequality does not change the direction of the inequality: if $ a < b $ and $ c \in \mathbb{R} $ then $ a + c < b + c $

— Subtracting the same real number (positive or negative) from each side of an inequality does not change the direction of the inequality: if $ a < b $ and $ c \in \mathbb{R} $ then $ a - c < b - c $

— Squaring each positive side of an inequality does not change the direction of the inequality: if $ 0 < a < b $ then $ a^2 < b^2 $

— Squaring each negative side of an inequality changes the direction of the inequality: if $ a < b < 0 $ then $ a^2 > b^2 $

— Inverting each (non-zero) side of an inequality changes the direction of the inequality: if $ a < b $ then $ \frac{1}{a} > \frac{1}{b} $

It is possible to merge several inequalities:

— Add member to member of inequalities of the same direction: if $ a < b $ and $ c < d $ then $ a+c < b+d $

— Multiply member by member of inequalities of the same direction: if $ 0 < a < b $ and $ 0 < c < d $ then $ a \times c < b \times d $

### What are allowed operators in an inequality?

Inequation operators allowed by the calculator are

— `<` (strictly inferior to, less than)

— `<=` (less than or equal to)

— `>` (strictly superior, greater than)

— `>=` (greater than or equal)

— `<>` or `!=`(different, not equal)

### How to solve an inequality step by step?

The calculating steps from the inequality solver are not displayed because the calculator is based on informatics operations that do not correspond to those of a hand-made resolution.

## Source code

dCode retains ownership of the "Inequality Solver" source code. Except explicit open source licence (indicated Creative Commons / free), the "Inequality Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Inequality Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Inequality Solver" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

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Cite as source (bibliography):

*Inequality Solver* on dCode.fr [online website], retrieved on 2024-07-02,

Summary

- Inequality solving
- What is an inequality? (Definition)
- How to solve an inequality?
- What are calculation techniques for solving inequalities?
- What are allowed operators in an inequality?
- How to solve an inequality step by step?

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Keywords

inequation,inequality,less,greater,inferior,superior,strict,strictly,equal,interval,calculator

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