Mechanics question

Hi, I found the critical value for k here, but is it less than or greater than this value? in my calculation I too friction as maximum, and as k increases the reaction force at A increases, so I assumed my calculated value is the maximum value for k, but the markscheme says otherwise. Thanks.

One of the suggested ways of working in the mark scheme is to proceed from Fa <= (mu)Ra (presented as F <= 0.35S in the mark scheme). If you work that way, the inequality for k will automatically come out the right way round at the end.

In the last line of working in the mark scheme there is a symbol that has come out as an empty square. I'm guessing that is meant to be ">=".