4/3r-3<r+2/3-1/3r..........

...........HELP ME PLEASE

the way you typed it and following the order of operation

I have to conclude that you mean

(4/3)r-3<r+2/3-(1/3)r
4r - 9 < 3r + 2 - r
2r < 11
r < 11/2

If it means something different, then you must include brackets.