SOLUTION: Solve the inequality -12<=-3x+6<=12

Question 29764: Solve the inequality -12<=-3x+6<=12

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
-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
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