Two simultaneously applied first-degree relationships in one variable constitute a system of first-degree inequalities in one variable.

### Properties

If the two inequalities are incompatible, there is no solution.

- Consider these inequalities:
*x*> 1 and*x*< 1; the solution set is ∅.

If the two inequalities are compatible, then there is a solution set.

- Consider these inequalities:
*x*> 1 and*x*< 3; the solution set is ]1, 3[.