Answer
Let $x$ be a non-integer real number. Then $\lfloor x\rfloor$ is the integer $n$ such that $n\leq x-n-1$. But since $-x$ is not an integer while $-n$ is an integer, we can further conclude that $-n-1\leq-x$
Work Step by Step
We can rigorously justify the assertion that $-n-1\leq-x$
