Finding the range of equation. Any tricks? I m working on the following problem 
For real numbers $a,b$, if $a+ab+b=3$, then find the range of $m=a-ab+b$. Is there any inequalities here to use?

You are given $a+ab+b=3$, which you can make $(a+1)(b+1)=4$.  Let $x=a+1, y=b+1$, so $xy=4$    $m=a-ab+b=x-1-(x-1)(y-1)+y-1=-xy+2x+2y-3=2x+2y-7=2x+\frac 8x-7$
Can you find the range of that?
