Question 29764
-12<=-3x+6<=12

-12<=-3x+6 
3x=<6+12 (grouping like terms,changing sign while changing side)
3x=<18
x=<6 ----(1) 
(dividing by the positive integer 3 and division by a positive quantity does not alter the inequality)

-3x+6<=12
-3x=<12-6 (grouping like terms,changing sign while changing side)
-3x=<6
x>=6/(-3) (dividing by the negative  integer 3 and division by a negative quantity  alters the inequality and so less than becomes greater  than and of course equality remains the same)
x>=-2  
That is -2< = x----(2)  

From (2) and (1) by transitivity
we have  -2 =<  x =<6