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

Nicely done! Ultimately, you don't need to consider the second case, since $\lvert t\rvert\neq t$ for $t<0,$ but it doesn't hurt to be thorough. The only thing to change about your conclusion is from $[1,\infty]$ to $[1,\infty),$ as "$\infty$" is a notational convention and not a real number.
