It is called **inequality** to one **algebraic inequality** in which its members are linked by **signs** **<** (smaller than), **≤** (less than or equal to), **>** (greater than) or **≥** (greater than or equal). In this way, inequalities are expressed as follows:

**f (x) <g (x)** or**f (x) ≤ g (x)** or**f (x)> g (x)** or**f (x) ≥ g (x)**

To solve an inequality, it is necessary to discover the **set of variable values** which allows to verify it. For example, let's take the inequality* 3x - 4 <8*. The resolution requires following steps as is done with the **equations** (which are equalities with numbers and letters related to each other through mathematical operations):

*3x - 4 <83x <12*

*x <4 *

In this inequality, we can notice that **x** is a value **less than 4** .

*3 x 3 - 4 <89 - 4 < 85 < 8*

or

*3 x 2 - 4 <86 - 4 < 82 < 8*

etc.

Instead, if we take the value **5** :

*3 x 5 - 4 <815 - 4 < 811 < 8* (which is not correct:

**11 is not less than 8**)

When two or more inequalities appear, there is talk of a **inequality system** . It is important to keep in mind that these are not always **systems** They have a solution.

You can differentiate between different systems of inequalities according to their **characteristics** . There are **first degree inequality systems** , the **second degree inequality systems** and the **systems of inequalities of degree greater than two** , among others.

To find the solution of an inequality system, you must arrive at the set of real numbers that allow the **check** of all the inequalities in question. That is to say that all inequalities must be resolved at the same time, otherwise the system will not be resolved.