So I have this basic absolute value problem: $|x-5|<|x+1$|. From what I understand, I need to consider what happens in every case. There are four cases, right? One where both sides are positive, one where both sides are negative and two where one side is negative and the other is positive.
The case were both are negative gives me something absurd ($5<-1$). Since the solution set is the intersection of the solutions for every case, this would mean that it has no solution. But it has.
Where is the error in my reasoning?