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# Inequalities practice

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Senior Manager
Joined: 08 Jan 2009
Posts: 326

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21 Feb 2009, 20:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What are the values of X that satisfy the inequality x+1/x < 2.5?

Ans :
1/2 < x < 2 .

But i felt x can also be any negative value.

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Senior Manager
Joined: 30 Nov 2008
Posts: 485

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Schools: Fuqua

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21 Feb 2009, 20:49
tkarthi4u,

Please go thru this link. Hope you will get some information on how to solve the Quadratic Inequalities.

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Intern
Joined: 10 Mar 2009
Posts: 3

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10 Mar 2009, 10:49
Hey mrsmarthi, i went through the link given for quad. eqns. It was of tremendous help.Thanks !!
I am posting my solution to the problem in this post using that method. Can you ( or anyone else perhaps) review it and tell me if it is indeed, the right way to go.

SOLUTION :
Since x+1/x<2.5,
I consider x+1/x-2.5<0 and further, i break it down to x+1/x-2.5 = y and y<0.

Now I solve the quadratic eqn considering y=0 i.e. x+1/x-2.5=0 and get the solution, (x-2)*(x-.5)=0.
Thus, on the number line, I plot the points .5 and 2 on the x -axis. We now have three regions on the x axis, which are
x>2, .5<x<2 and x<.5.

Now, for the main equation, we need to see y<0 lies in which of the three regions.
x+1/x-2.5 =0 can be written as x^2-2.5x+1=0. We can find the vertex of the parabola using the formula, v=(-b/2a,c-b^2/4a).
Which gives us v below the x -axis between .5 and 2 and .5 and 2 are the x-intercepts of the parabola.

Thus, between .5 and 2, the parabola x+1/x-2.5 or simply y is less than zero.

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SVP
Joined: 28 Dec 2005
Posts: 1545

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10 Mar 2009, 17:19
Can I ask a question on this :

x+1/x < 2.5 can be rewritten as 1+1/x < 2.5 --> 1/x <1.5 --> x>2/3

where did i go wrong ?

Kudos [?]: 178 [0], given: 2

Senior Manager
Joined: 30 Nov 2008
Posts: 485

Kudos [?]: 360 [0], given: 15

Schools: Fuqua

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11 Mar 2009, 07:31
One VERY VERY IMP thing to remember in Inequalities -

DO NOT multiple,divide variable on both sides of the Inequality.(The reason being we don't know the sign of x and depending ont he sign, the inequality will change. )

How ever we can add / subtract a variable on both sides of the Inequality.

pmenon wrote:
Can I ask a question on this :

x+1/x < 2.5 can be rewritten as 1+1/x < 2.5 --> 1/x <1.5 --> x>2/3

where did i go wrong ?

Hilighted part is incorrect. It should translate to --> x + 1/x <2.3 ==> (x^2 + 1) / x < 2.5.

Hope you got the mistake.

Kudos [?]: 360 [0], given: 15

Re: Inequalities practice   [#permalink] 11 Mar 2009, 07:31
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