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\left(x-1\right)\times 2=x-3
Variable x cannot be equal to any of the values 1,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x-1\right), the least common multiple of x-3,x-1.
2x-2=x-3
Use the distributive property to multiply x-1 by 2.
2x-2-x=-3
Subtract x from both sides.
x-2=-3
Combine 2x and -x to get x.
x=-3+2
Add 2 to both sides.
x=-1
Add -3 and 2 to get -1.