Solve the following inequalities (where `[*]` denotes greatest integer function and `{*}` represent fractional part function)
`(i) [x+[x]] lt 0` `(ii) [2x^(2)-x] lt 1` `(iii) {x} lt (1)/(2)`

Answer

`(i) x in (-oo,0)` `(ii) x in ((-1)/(2),1)` `(iii) x in uuu_(n in I)[n,n+(1)/(2))`