A website Maths Puzzle Logical Reasoning

Find the mistake in these mathematical equations.
x = 2
x(x-1) = 2(x-1)
x2-x = 2x-2
x2-2x = x-2
x(x-2) = x-2
x = 1

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A website Other Question

These are the conditions in Baldyville:

No two inhabitants have the same number of hairs on their head.
No inhabitant has exactly 518 hairs.
There are more inhabitants in town than hairs on any individual inhabitant's head.
What is the highest possible number of inhabitants?
Here's a variation on a famous puzzle by Lewis Carroll, who wrote Alice's Adventures in Wonderland.
A group of 100 soldiers suffered the following injuries in a battle: 70 soldiers lost an eye, 75 lost an ear, 85 lost a leg, and 80 lost an arm.
What is the minimum number of soldiers who must have lost all 4?