How do I solve this |2x-1|-|x|< 4 ? Do i simply treat it like an equation, meaning that it has three different solutions? or do other rules apply?
the first element is positive if x > 0.5 and negative otherwise, the second element is positive if x > 0 and negative otherwise.
1. x => 0.5, in this range both elements are non negative so:
2x-1 - x < 4
x < 5
so the solution is: 0.5 <= x < 5
2. 0 <= x <= 0.5 in this range the first element is negative and the second is non negative so:
-(2x-1) - x < 4
x > -1
thus the answer is 0 <= x <= 0.5
3. x <= 0 in this range the first element is negative and the second is non positive so:
-(2x-1) + x < 4
x > -3
thus the solution is -3 < x <= 0
The final solution is the intersection of these 3 solutions thus:
-3 < x < 5