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# Find the range of values of x that satisfy the inequality (x - 3)^2

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Joined: 04 Jan 2015
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Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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Updated on: 28 Jul 2019, 21:40
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45% (medium)

Question Stats:

72% (01:42) correct 28% (02:03) wrong based on 308 sessions

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Wavy Line Method Application - Exercise Question #2

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

A. x > 1
B. x > -3
C. -1 < x < 3
D. x < -3 or -1 < x < 3
E. x < -3

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, 02:32.
Last edited by Bunuel on 28 Jul 2019, 21:40, edited 4 times in total.
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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26 Aug 2016, 09:55
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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: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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17 Nov 2016, 08:40
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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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Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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Updated on: 07 Aug 2018, 06:46
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1
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, 02:36.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:46, edited 1 time in total.
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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31 Jul 2017, 00:45
@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: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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30 Aug 2018, 06:39
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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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Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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27 Jul 2019, 07:28
hatemnag wrote:
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.

Hello! Following this method, eqns will be (x-3)^3 (x+1) ^5 (x+3) < 0
=> x < 3 or x<-3 or x<-1 (x+1) = 0
So how did you decipher that x >-1 ?
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Joined: 31 Jul 2019
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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01 Oct 2019, 18:29
how to decide the direction of the graph? whether it would start from the negative or positive?
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Joined: 16 Aug 2019
Posts: 2
Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

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05 Oct 2019, 10:58
How to decide the direction of graph?
Can't we have the ranges as -3<x<-1 or x>3 ?
Re: Find the range of values of x that satisfy the inequality (x - 3)^2   [#permalink] 05 Oct 2019, 10:58
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