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What does x equal if 5/x=9/2x

Mathematics
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no value of x satisfies that. because if you rearrange it you would get x=10x/5 as you know no number can be defined like that unless it is 0
the x terms on both sides gets cancelled leaving away no solution
That is the solution-- but I am curious why can't you make it x=9/10x? and then go from there 10x^2=9 x^2=9/10 x=3/sqrt10

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Other answers:

5/x=9/2x multiply both sides by x 5=9/2???? no solution
Why can't you multiply both sides by 1/5 instead of x?
an unreal solution would be x=infinity infact 2 unreal solutions -> inf and -inf
  • hba
There would be infinite solutions ? @shubhamsrg or no solutions ?
  • hba
I guess they are infinite solutions.
No sol.
I understand the answer is no solution--- what I am asking is why can't you divide by 5 to get x by itself.
2 solns, 2 unreal solutions, or should i say 2 theoretical solutions.
  • hba
I guess we should call it infinite solutions.
no @hba
hmm ? I'd still say 2 solutions which are inf and -inf , but both are theoretical .
  • hba
@saifoo.khan Explain. I remember hero telling me that there would be infinite solutions. I also believed there would be no solution.
Will one of you brilliant people just explain what algebraic rule I am missing/perverting that is making me not see the no solution. Why can't you multiply by 1/5?
  • hba
@sleipnir234 Ok Lets follow you, \[\huge\frac{ 5 }{ x }=\frac{ 9 }{ 2x }\] Now multiply and divide by 1/5. Let us see what you get.
  • hba
Now multiply both sides by 1/5 *
  • hba
\[\frac{ 5 }{ x } \times \frac{ 1 }{ 5 }=\frac{ 9 }{ 2x } \times \frac{ 1 }{ 5 }\]
x=9/10x
if you multiply both sides by 1/5, you get 1/x =9/(10x) and not x=9/10x
if there is an identity after cancelling 'x', then there are infinite solutions @hba, here we don't get an identity, ,we get 1=9/10 which is NEVER tru , so, no solution. if we got something like 1=9/9, then we would have infinite solutions
  • hba
@hartnn Thanks for explaining :)
ohhhhhhhhh Got it. Thank you so much. I'm sorry. It is late. And I am an idiot. Thank you all so much for being patient!!
There are, 2 solutions! 2 theoretical solutions, one should not ignore that.
  • hba
Welcome :)
silly mistakes usually happen,no problem, welcome ^_^

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