Always or Never

An absolute value is never negative, so some of these inequalities can be answered without any splitting. The inequality |x| < -1 asks for a distance smaller than a negative number. No number has one, so there is no solution. The inequality |x - 4| > -2 asks for a distance greater than a negative number. Every distance is at least 0, so this is true for every x.

These cases also appear after you isolate the absolute value. For example, |x + 2| + 3 < 1 becomes |x + 2| < -2, which has no solution. The sign of the number the absolute value is compared with decides the answer. So isolate first, and look at that sign before you split anything.