Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

5/x=9/2x
multiply both sides by x

5=9/2???? no solution

Answer 5

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

Answer 6

an unreal solution would be x=infinity
infact 2 unreal solutions -> inf and -inf

Answer 7

There would be infinite solutions ? @shubhamsrg or no solutions ?

Answer 8

I guess they are infinite solutions.

Answer 9

No sol.

Answer 10

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

Answer 11

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

Answer 12

I guess we should call it infinite solutions.

Answer 13

no @hba

Answer 14

hmm ? I'd still say 2 solutions which are inf and -inf , but both are theoretical .

Answer 15

@saifoo.khan Explain.

I remember hero telling me that there would be infinite solutions.

I also believed there would be no solution.

Answer 16

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?

Answer 17

@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.

Answer 18

Now multiply both sides by 1/5 *

Answer 19

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

Answer 20

x=9/10x

Answer 21

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

Answer 22

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

Answer 23

@hartnn

Thanks for explaining :)

Answer 24

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!!

Answer 25

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

Answer 26

Welcome :)

Answer 27

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