If -1 < 2y < 0, what are the possible values of |y| - y ?
(|y| is the absolute value of y)
I know the interval is 0 < y < 1 but I don't how to show it algebraically..
You are given $\displaystyle -1<2y<0$.
Divide by two: $\displaystyle -0.5<y<0$. Multiply by $\displaystyle -1:~~0<-y<0.5$.
If you know that $\displaystyle -3<a<-1$ then $\displaystyle 1<|a|<3$. So from the given $\displaystyle 0<|y|<0.5$.
Add those two together: $\displaystyle 0<|y|-y<1~.$