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-4x+9-2x<-27
Subtract 2x from both sides.
-6x+9<-27
Combine -4x and -2x to get -6x.
-6x<-27-9
Subtract 9 from both sides.
-6x<-36
Subtract 9 from -27 to get -36.
x>\frac{-36}{-6}
Divide both sides by -6. Since -6 is negative, the inequality direction is changed.
x>6
Divide -36 by -6 to get 6.