On solving
$$-2 < \frac{-a}{a-2} \qquad \text{and} \qquad\frac{-a}{a-2}<1$$ I get $$ 2a-4> a \qquad \text{and} \qquad-2a<-2 $$ which implies that $a>4$ and $a>1$. However this is part of a bigger question whose final result is that $a$'s value range is from negative infinity to $-\frac14$ and this does not correspond to that. What is wrong in my approach and what am I doing wrong?