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