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

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EgmatQuantExpert
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Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   Updated on: 28 Jul 2019, 21:40
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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


Show Spoiler
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.

To read all our articles: Must read articles to reach Q51

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D

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] New post   Updated on: 07 Aug 2018, 06:46
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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

Correct Answer: Option D


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] New post   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:: https://gmatclub.com/forum/wavy-line-method-application-complex-algebraic-inequalities-224319.html


Detailed solution will be posted soon.


Please post the options also.

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] New post   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.
Please Payal correct my answer if something is wrong
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   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] New post   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] New post   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.
Please Payal correct my answer if something is wrong




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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Re: Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   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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Re: Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   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 ?
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   20 Feb 2020, 07:54
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

Correct Answer: Option D



Hi Payal,
Can you please help me? According to egmat tutorial whenever power is even the wavy line bounce back and it will not cross the zero point, but here the power of (x-3) is even, so if we start from the top right corner how it can cross the zero point and came into the -ve region?

Regards,
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   23 May 2021, 09:35
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

Correct Answer: Option D



Wavy line approach is pretty cool.

My question is..

After i arrange the intersections points aka Roots,
How do i start the wave.

Is it always starting from below X axis - upward curve?

I tried few sources but everyone has a different approach and this concept is not yet clear.
Bunuel VeritasKarishma

Posted from my mobile device
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   23 May 2021, 09:37
agar123 wrote:
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

Correct Answer: Option D



Hi Payal,
Can you please help me? According to egmat tutorial whenever power is even the wavy line bounce back and it will not cross the zero point, but here the power of (x-3) is even, so if we start from the top right corner how it can cross the zero point and came into the -ve region?

Regards,



That's because ( X²- 9 ) =( x-3)(x+3) hence the power of

(X-3)³

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Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink] New post   Updated on: 27 Nov 2023, 23:51
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Hemanthdasu13 wrote:
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

Correct Answer: Option D



Wavy line approach is pretty cool.

My question is..

After i arrange the intersections points aka Roots,
How do i start the wave.

Is it always starting from below X axis - upward curve?

I tried few sources but everyone has a different approach and this concept is not yet clear.
Bunuel VeritasKarishma

Posted from my mobile device



Hemanthdasu13

Follow one style else you will mix them up.
Here is the step by step process I follow: https://youtu.be/PWsUOe77__E

Originally posted by KarishmaB on 24 May 2021, 00:40.
Last edited by KarishmaB on 27 Nov 2023, 23:51, 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] New post   14 Jul 2023, 09:12
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EgmatQuantExpert wrote:
Wavy Line Method Application - Exercise Question #2


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


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


Show Spoiler
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.

To read all our articles: Must read articles to reach Q51



Responding to a pm:

First check out how the inequalities are represented on the number line here: https://www.youtube.com/watch?v=VnEVS8kmWa8

Next, we can use the wavy line method to solve this.
\((x - 3)^2 (x + 1)^5 (x^2 - 9) < 0\)
\((x - 3)^2 (x + 1)^5 (x + 3)(x - 3) < 0\)
Factors with even exponents are taken as constants. Factors with positive odd exponents are taken as if they have an exponent of 1.

Hence transition points are -3, -1 and 3 only.

Since we are looking for negative values of the expression, we see that x < -3 or -1 < x < 3

Answer (D)
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Re: Find the range of values of x that satisfy the inequality (x - 3)^2 [#permalink]
14 Jul 2023, 09:12
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