Find the integral solutions of the inequality $$|2x-3|-|x| \le 3$$ The solutions i found out were $0,2,3,4,5,6.$But how do i find 1 as a solution to it ? I'm now fully confused of the cases. The solution 2,3,4,5,6 came out from the condition when $x \gt 3/2$. The solution x=0 came up in the case $x \le 0$. But in the case $0\lt x \lt 3/2 $, i get the following expression, $$3-2x-x \lt 3$$which simplifies to $$-3x \lt 0$$or $x \lt 0$. But the given condition inequality does not satisfy in the case we took. So how do i find x=1 as an answer ?