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2+x=2\left(1+x\right)
Multiply both sides of the equation by 2y, the least common multiple of 2y,y.
2+x=2+2x
Use the distributive property to multiply 2 by 1+x.
2+x-2x=2
Subtract 2x from both sides.
2-x=2
Combine x and -2x to get -x.
-x=2-2
Subtract 2 from both sides.
-x=0
Subtract 2 from 2 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -1 is not equal to 0, x must be equal to 0.