- anonymous

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

- katieb

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- anonymous

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

- AravindG

the x terms on both sides gets cancelled leaving away no solution

- anonymous

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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## More answers

- AravindG

5/x=9/2x
multiply both sides by x
5=9/2???? no solution

- anonymous

Why can't you multiply both sides by 1/5 instead of x?

- shubhamsrg

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.

- saifoo.khan

No sol.

- anonymous

I understand the answer is no solution--- what I am asking is why can't you divide by 5 to get x by itself.

- shubhamsrg

2 solns, 2 unreal solutions, or should i say 2 theoretical solutions.

- hba

I guess we should call it infinite solutions.

- saifoo.khan

no @hba

- shubhamsrg

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.

- anonymous

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

\[\frac{ 5 }{ x } \times \frac{ 1 }{ 5 }=\frac{ 9 }{ 2x } \times \frac{ 1 }{ 5 }\]

- anonymous

x=9/10x

- hartnn

if you multiply both sides by 1/5, you get
1/x =9/(10x)
and not x=9/10x

- hartnn

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 :)

- anonymous

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!!

- shubhamsrg

There are, 2 solutions!
2 theoretical solutions, one should not ignore that.

- hba

Welcome :)

- hartnn

silly mistakes usually happen,no problem, welcome ^_^

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