Let $⌊x⌋$ denote the integer part of $x$ and let $a$ be a real number.
My questions are:
(1) Find sufficient and necessary conditions for which the inequality: $$⌊x⌋<x-a$$ is possible
(2) Solve that inequality with respect to $x$.
My attempt: I can think that when $0<a<1$, the inequalty is possible. But I cannot go further on that.