Solving inequalities

[Vikash]

How do you solve an inequality like this : x^-1/2-9x^-3/2<0

 

[Vikash]

Help is REALLY APPRECIATED!

How do you solve an inequality like this : x^-1/2-9x^-3/2<0

 

[pka]

How do you solve an inequality like this : x^-1/2-9x^-3/2<0

Note the $x\cancel\le 0$ Can you explain why?
Looking at the factored form $x^{-\frac{3}{2}}(x-9)<0$ we can see that $0<x<9$.

 

[Deleted member 4993]

How do you solve an inequality like this : x^-1/2-9x^-3/2<0

Screaming does not help - showing your will!

You have been told to show your work before (such as in: https://www.freemathhelp.com/forum/threads/modelling-with-geometric-sequences.125212/)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Steven G]

I'd get a common denominator then ....

 

[Vikash]

Note the $x\cancel\le 0$ Can you explain why?
Looking at the factored form $x^{-\frac{3}{2}}(x-9)<0$ we can see that $0<x<9$.

A more detailed explanation pleaseee?

 

[pka]

A more detailed explanation pleaseee

SEE HERE.

 

[Steven G]

x^-1/2 - 9x^-3/2 = 1/x^1/2 - 9/x^3/2 = x/x^3/2 - 9/x^3/2 =(x-9)/x^3/2 < 0