Always or Never

An absolute value is never negative, so some of these inequalities can be answered without any splitting. The inequality $\left|x\right| < -1$ asks for a distance smaller than a negative number. No number has one, so there is no solution. The inequality $\left|x-4\right| > -2$ 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, $\left|x+2\right|+3 < 1$ becomes $\left|x+2\right| < -2$, 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.