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 <8 x <4
In this inequality, we can notice that x is a value less than 4 .
3 x 3 - 4 <8
9 - 4 < 8
5 < 8
3 x 2 - 4 <8
6 - 4 < 8
2 < 8
Instead, if we take the value 5 :
3 x 5 - 4 <8
15 - 4 < 8
11 < 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.