write an absolute value inequality that has no solution.?

Answer 1

|x| < -5

This has no solution because the absolute value of x is always greater than or equal to zero (that is, it is never negative).

Answer 2

|x|<0
|x^2+x +14|<0
In short:
|f(x)|<0
Another example can be:
|(x+y)^2|<|x^2|+|y^2|

Answer 3

|x| < -82