Solve the equation |x-1|=x-1 Solve the equation:$|x-1|=x-1$
My solution:
Case 1 :$ x\ge1$, Hence $x-1=x-1$, therefore infinite solution
Case 2 :$ x<1$, Hence $1-x=x-1$,$x=1$, hence no solution
But the solution i saw concept used is $ x\le1$ in lieu of $ x<1$
Hence final answer is $[1,\infty]$, is this concept correct

Your answer is right, apart from the square bracket pointed out in @ElevenEleven's comment ($\infty$ can't be the upper end of a closed interval).
Another way to get it is to note that $|a|=a$ only when $a\geq 0$, so for $a=x-1$,
$$|x-1|=x-1$$ implies $$x-1\geq 0$$
which gives you the answer without needing to consider different cases.
