Negative four times a number plus nine is no more than the number minus twenty one

4x+9 =< x-21 
-4x-x +9 =< x-x-21 
-5x +9 =< -21 
-5x +9-9 =< -21-9 
-5x =< -30 
-5x/-5 =< -30/-5 (DANGER divide by neg affects direction of inequality) 
x =< 6 
CHECK sign 
-4x+9 =< x-21 
-4*6+9 =< 6-21 
-24+9 =<-15 
-15 =<-15 

-4*7+9 =< 7-21 
-28+9 =< 7-21 
-19 =< -14 false 

-4*5+9 =< 5-21 
-20+9 =< -16 
-11 =< -16 true 

so 
x =< 6 is correct. 

I use =< since eq would NO MORE THAN.