Eyes down

The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?

Problem



The symbol [ ] means 'the integer part of '.

Consider the three numbers

$$[2x];\ 2[x];\ [x + {1\over 2}] + [x - {1\over 2}]$$

Can they ever be equal?

Can they ever take three different values?