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

Inequality Solver - dCode

Tag(s) : Symbolic Computation

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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.

**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} $
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- 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 $

**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)

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.

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

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Source : https://www.dcode.fr/inequality-solver

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