Question

I can prove that 2=1, where is the error?

X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1

I subtracted -2
because thats the # I chose to subtract with.

Answer 1

Answer:The algebraic steps you have taken are incorrect, leading to an invalid conclusion. Let's go through each step and see where the mistake is made:

X = 1 (given)

X+X = 1+X (adding X to both sides)

2X = 1+X (combining like terms)

2X = X+1 (rearranging terms)

2X-2 = X+1-2 (subtracting 2 from both sides)

2X-2 = X-1 (simplifying)

2(x-1)/(x-1) = (x-1)/(x-1) (dividing both sides by x-1, note that x cannot be 1 as it would result in division by 0)

2 = 1 (canceling out the (x-1)/(x-1) on both sides)

The error lies in dividing both sides by (x-1) in step 7. Although (x-1) appears on both sides of the equation, it is not equal to zero as x cannot be 1 due to division by zero. Dividing by (x-1) effectively cancels it out, leading to the incorrect result of 2=1.

Explanation: