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?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

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?