OR compound inequalities

Question

Can a compound inequality with OR be No Solution or can an OR compound inequality never be No Solution 

Answer 1

This looks more like a logic problem.  It is possible to have no solution if both conditions in the OR statement are false.  Consider an example:

 

Solve for all real values of x that satisfy

 

|x| < -1 OR x² < 0

 

Both parts are false, so the entire inequality is false.  It has no solution.  Now consider:

 

Solve for all real values of x that satisfy 

 

|x| < -1 OR |x| ≥ 0

 

The left part is false, but the right part is true, so the right part has solutions.  To be true, an OR statement needs only one part of it to be true.  To be false, an OR statement needs every part of it to be false.