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6x+3-x<0
Subtract x from both sides.
5x+3<0
Combine 6x and -x to get 5x.
5x<-3
Subtract 3 from both sides. Anything subtracted from zero gives its negation.
x<-\frac{3}{5}
Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.