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2x-2+x<x
Subtract 3 from 1 to get -2.
3x-2<x
Combine 2x and x to get 3x.
3x-2-x<0
Subtract x from both sides.
2x-2<0
Combine 3x and -x to get 2x.
2x<2
Add 2 to both sides. Anything plus zero gives itself.
x<\frac{2}{2}
Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.
x<1
Divide 2 by 2 to get 1.