this is about squaring both side for an absolute inequalities on only one side problem. For example:
$|6-2x|< x+4$ when solved both by squaring both sides and by defining it$ -(x+4)<6-2x< x+4$. they both give the same answer.
But for $|x+1|<2x+5$ squaring both side give out answer: $x<-4$ and $x>-2$ ;
by defining it $-(2x+5)< x+1<2x+5$, it give out answer: $x>-2$ only.
and when i check for $x<-4$ using $x=-5$, the solution for $x<-4$ contradict $|x+1|<2x+5$.
So, how do we know if the expression can be solved by squaring both sides? thank you