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4x+3-6x<-9
Subtract 6x from both sides.
-2x+3<-9
Combine 4x and -6x to get -2x.
-2x<-9-3
Subtract 3 from both sides.
-2x<-12
Subtract 3 from -9 to get -12.
x>\frac{-12}{-2}
Divide both sides by -2. Since -2 is negative, the inequality direction is changed.
x>6
Divide -12 by -2 to get 6.