Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

I am 5 letters long.
My first two tell you who I am
My first 3 could be a medicine
My last three reversed could be a young boy.
My 4th, 3rd and 2nd in that order could be a fruit drink.
If you have me you may hang me round your neck
WHAT AM I ?

Which statement is true out of the following?
One statement here is false.
Two statements here are false.
Three statements here are false.

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

How many cubic feet of dirt are in a hole of one foot deep, three feet long, and two feet wide?

I can sizzle like bacon,
I am made with an egg,
I have plenty of backbone, but lack a good leg,
I peel layers like onions, but still remain whole,
I can be long, like a flagpole, yet fit in a hole.

In 1990, a person is 15 years old. In 1995, that same person is 10 years old. How can this be?