What do I do if a compound inequality contradicts itself? Do I put down empty set, or what?
yes
Ok, -3<x<-2
x is cannot be greater than -2 but less than -2. x belongs to the empty solution set.
If a compound inequality contradicts itself, it means that there is no solution that satisfies the given conditions. In such a case, the solution set would be considered empty.
To understand why the compound inequality contradicts itself, you can follow these steps:
1. Begin by solving each inequality separately. This will help you understand the individual constraints.
2. Analyze the solutions to each inequality and determine if there is an overlap or intersection between the two sets.
3. If the two sets have no common values or overlap, it means there is no solution that satisfies both inequalities simultaneously.
4. In such cases, you can represent the empty solution set using the mathematical notation Ø or ∅. This indicates that there are no values that simultaneously satisfy the compound inequality.
Remember, the empty set (∅) indicates that the compound inequality has no solution and should be used only when there is no intersection between the solutions to the two separate inequalities.