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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 -

Tag(s) : Symbolic Computation

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# Inequality Solver

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## Inequality solving

 Solving Domain Set R (Reals) Z (Integers) C (Complex)

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

## Answers to Questions

### How to solve an inequality?

dCode can solve all inequalities and find variables.

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 N 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 $a \frac{b}{c}$

- 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 alowed by the calculator are

- < (strictly inferior to, less than)

- <= (less than or equal to)

- > (strictly superior, greater than)

- >= (greater than or equal)

- <> (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 online 'Inequality Solver' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script, copy-paste, or API access will be for free, same for Inequality Solver download for offline use on PC, tablet, iPhone or Android !

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## Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Inequality Solver' tool, so feel free to write! Thank you!

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