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# Wavy Line Method Application - Exercise Question #2

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Wavy Line Method Application - Exercise Question #2  [#permalink]

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Updated on: 07 Aug 2018, 05:45
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Wavy Line Method Application - Exercise Question #2

Find the range of values of x that satisfy the inequality $$(x - 3)^2 (x + 1)^5 (x^2 - 9) < 0$$

Wavy Line Method Application has been explained in detail in the following post:: Wavy Line Method Application - Complex Algebraic Inequalities

Detailed solution will be posted soon.

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Originally posted by EgmatQuantExpert on 26 Aug 2016, 01:32.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:45, edited 2 times in total.
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Re: Wavy Line Method Application - Exercise Question #2  [#permalink]

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26 Aug 2016, 08:55
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EgmatQuantExpert wrote:
Wavy Line Method Application - Exercise Question #2

Find the range of values of x that satisfy the inequality $$(x - 3)^2 (x + 1)^5 (x^2 - 9) < 0$$

Wavy Line Method Application has been explained in detail in the following post:: http://gmatclub.com/forum/wavy-line-method-application-complex-algebraic-inequalities-224319.html

Detailed solution will be posted soon.

Solving the inequality, we will get (x-3)^2(x+1)^5(x+3)(x-3) < 0

or (x-3)^3 (x+1)^5 (x+3) < 0.

Solving on the number line, we will get the points -3,-1 and 3.

Since the power of each is ODD. hence, the range of x will be (-infinity, -3) U (-1,3).

Please correct me if I am missing anything.
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Re: Wavy Line Method Application - Exercise Question #2  [#permalink]

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17 Nov 2016, 07:40
I guess the final answer is : -1< X <3 & x <-3
since the zero points are 3 , -1 , -3
if we try each number within the range , the inequality will hold true, using the detailed equation :
(x-3)(x-3)(x+1)(x+3)(x-3)<0
But I propose to ignore the even powered expression like the case of (x-3) since the product of such expression must be positive.
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Wavy Line Method Application - Exercise Question #2  [#permalink]

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Updated on: 07 Aug 2018, 05:46
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Solution:

Hey Everyone,

Please find below, the solution of the given problem.

Rewriting the inequality to easily identify the zero points

$$(x-3)^2 (x+1)^5 (x^2-9)<0$$

Since

$$(x^2-9)=(x+3)*(x-3)$$

The given inequality can be written as

$$(x-3)^3 (x+1)^5 (x+3)<0$$

Plotting the zero points and drawing the wavy line:

Required Range: x < -3 or -1 < x < 3

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Originally posted by EgmatQuantExpert on 18 Nov 2016, 01:36.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:46, edited 1 time in total.
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Re: Wavy Line Method Application - Exercise Question #2  [#permalink]

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30 Jul 2017, 23:45
@e-gmat team

Is it by any chance possible that all the powers are even and hence the wavy line bounces back for all the points?
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Re: Wavy Line Method Application - Exercise Question #2  [#permalink]

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30 Aug 2018, 05:39
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Shiv2016 wrote:
@e-gmat team

Is it by any chance possible that all the powers are even and hence the wavy line bounces back for all the points?

If all the powers are zero then the equation never becomes less than zero.
e.x: (x-3)^4(x+6)^6(x-1)^2<0
here the minimum value of the inequality is 0, for no value of x the equation becomes less than zero.
no solution is the answer in such case.
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Wavy Line Method Application - Exercise Question #2  [#permalink]

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30 Aug 2018, 06:52
EgmatQuantExpert wrote:
Solution:

Hey Everyone,

Please find below, the solution of the given problem.

Rewriting the inequality to easily identify the zero points

$$(x-3)^2 (x+1)^5 (x^2-9)<0$$

Since

$$(x^2-9)=(x+3)*(x-3)$$

The given inequality can be written as

$$(x-3)^3 (x+1)^5 (x+3)<0$$

Plotting the zero points and drawing the wavy line:

Required Range: x < -3 or -1 < x < 3

EgmatQuantExpert you say option D, where are answer choices ? btw based on my gmat prep I noticed most correct answer choices are DDDDDD s pls share your experience with us one sec approach if you dont see answer choices click D and move on
Wavy Line Method Application - Exercise Question #2 &nbs [#permalink] 30 Aug 2018, 06:52
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