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3x-\left(x-1\right)=2
Multiply both sides of the equation by 6, the least common multiple of 2,6,3.
3x-x-\left(-1\right)=2
To find the opposite of x-1, find the opposite of each term.
3x-x+1=2
The opposite of -1 is 1.
2x+1=2
Combine 3x and -x to get 2x.
2x=2-1
Subtract 1 from both sides.
2x=1
Subtract 1 from 2 to get 1.
x=\frac{1}{2}
Divide both sides by 2.