Laughing
This is not unique - just bad algebra!!
5x = 10x → 10x - 5x = 0 → 5x = 0 → x = 0
What is there to get confused about?!!
Tsk, Tsk. Sir, I think you have lost the ability to see what others do not see. Alas, you probably lost your ignorance at an early age, but hey, don't be embarrassed, it happens! (I hope you have a sense of humor.)
To no one in particular ... How about this for a junior/intermediate algebra problem?
---
"Given that x = 1 is the solution to an equation, what is THE equation that produces that solution?"
Correct the above sentence so that it makes sense, illustrate with examples.
(Oblique clue, what a difference an article makes.)
---
Really, I think that such a question, offering as it does, a "reverse engineering approach" leads to a significant insight, but, you know, maybe not.
(Mr Denis, thanks, and, x<>0, yeah!)