If lx - 1 l = lx - 2 l
then x = ?
If,
$\displaystyle x-2\geq 0$ then $\displaystyle x-1\geq 0$ thus,
$\displaystyle x-2=x-1$---- Emptry solution set.
If,
$\displaystyle x-1<0$ then $\displaystyle x-2<0$
Thus,
$\displaystyle 1-x=2-x$---- Empty solution set.
If,
$\displaystyle x-2<0$ and $\displaystyle x-1\geq 0$ (1<= x< 2)
Then,
$\displaystyle 1-x=x-2$
Thus,
$\displaystyle x=3/2$