x-1 >(or equal) 6/x
x-1>=6/x
which looks like an inequality already solved on this site, recently;
--------critical x values are -2, 0, 3.
INTERVALS TO CHECK
(-infin, -2] [-2, 0) (0,3] [3, infin)
sign (-)(-)/(-)=- (-)(+)/(-)=+ (-)(+)/(+)=- (+)(+)/(+)=+
value FALSE TRUE FALSE TRUE
The solution set will be all the intervals which make the inequality true.
This is [-2,0) AND [3,infinity).
(The intervals should really be checked using the original inequality).