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1-2x=2\left(x-2\right)
Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2, the least common multiple of x-2,2-x.
1-2x=2x-4
Use the distributive property to multiply 2 by x-2.
1-2x-2x=-4
Subtract 2x from both sides.
1-4x=-4
Combine -2x and -2x to get -4x.
-4x=-4-1
Subtract 1 from both sides.
-4x=-5
Subtract 1 from -4 to get -5.
x=\frac{-5}{-4}
Divide both sides by -4.
x=\frac{5}{4}
Fraction \frac{-5}{-4} can be simplified to \frac{5}{4} by removing the negative sign from both the numerator and the denominator.