sleipnir234 2 years ago What does x equal if 5/x=9/2x

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1. sampatho2

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

2. AravindG

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

3. sleipnir234

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

4. AravindG

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

5. sleipnir234

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

6. shubhamsrg

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

7. hba

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

8. hba

I guess they are infinite solutions.

9. saifoo.khan

No sol.

10. sleipnir234

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

11. shubhamsrg

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

12. hba

I guess we should call it infinite solutions.

13. saifoo.khan

no @hba

14. shubhamsrg

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

15. hba

@saifoo.khan Explain. I remember hero telling me that there would be infinite solutions. I also believed there would be no solution.

16. sleipnir234

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?

17. 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.

18. hba

Now multiply both sides by 1/5 *

19. hba

$\frac{ 5 }{ x } \times \frac{ 1 }{ 5 }=\frac{ 9 }{ 2x } \times \frac{ 1 }{ 5 }$

20. sleipnir234

x=9/10x

21. hartnn

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

22. 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

23. hba

@hartnn Thanks for explaining :)

24. sleipnir234

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!!

25. shubhamsrg

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

26. hba

Welcome :)

27. hartnn

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