I'm having a problem with this question:
For which values of the real parameter a the equation:
has exactly 4 solutions?
The solution is this: $$0 < a < 1$$
What I tried was this:
1) Make the first condition, $a>0$,
Split the equation in these two: $(1)~|x|-1=a;~(2)~|x|-1=-a$.
2) Make the second conditions, $(1)~a+1>0,~a>-1; (2)~-a+1>0,~a<1$
If the conditions are true, the equation will have 4 solutions, therefore, a is contained in the interval $<0,1>$, which is $0 < a < 1$.
Was the described procedure correct?
Thanks in advance.