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Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
Updated on: 28 Jul 2019, 21:40
Updated on: 28 Jul 2019, 21:40
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based on 868
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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
_________________
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.
To read all our articles: Must read articles to reach Q51
Detailed solution will be posted soon.
To read all our articles: Must read articles to reach Q51
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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.
Last edited by Bunuel on 28 Jul 2019, 21:40, edited 4 times in total.
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
Updated on: 07 Aug 2018, 06:46
Updated on: 07 Aug 2018, 06:46
2
Kudos
5
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Expert Reply
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
_________________
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
_________________
Free Trial: Get 25 AI powered videos | 400 practice questions | 8 free webinars
Case studies: How a personalized study plan can save you 60+ hours
MBA admits: M7 admits | INSEAD admits | ISB admits [40+ case studies]
Learn why e-GMAT has 10X more 700+ verified scores than other GMATClub partners – Read our 2000+ reviews
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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.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:46, edited 1 time in total.
General Discussion
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
26 Aug 2016, 09:55
26 Aug 2016, 09:55
3
Kudos
Expert Reply
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.
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]
17 Nov 2016, 08:40
17 Nov 2016, 08:40
1
Kudos
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
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
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
31 Jul 2017, 00:45
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?
Is it by any chance possible that all the powers are even and hence the wavy line bounces back for all the points?
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
30 Aug 2018, 06:39
30 Aug 2018, 06:39
1
Kudos
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?
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.
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
27 Jul 2019, 07:28
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
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 ?
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
01 Oct 2019, 18:29
01 Oct 2019, 18:29
how to decide the direction of the graph? whether it would start from the negative or positive?
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
05 Oct 2019, 10:58
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 ?
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]
20 Feb 2020, 07:54
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
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,
Senior Manager
Joined: 04 May 2020
Status:What goes round comes around, so does Kudos.
Posts: 262
Location: India
GPA: 4
WE:Business Development (Retail Banking)
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
23 May 2021, 09:35
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
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
Senior Manager
Joined: 04 May 2020
Status:What goes round comes around, so does Kudos.
Posts: 262
Location: India
GPA: 4
WE:Business Development (Retail Banking)
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
23 May 2021, 09:37
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
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
Posted from my mobile device
Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
Updated on: 27 Nov 2023, 23:51
Updated on: 27 Nov 2023, 23:51
1
Kudos
Expert Reply
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
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
_________________
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ANA PREP BLOG, Private Tutoring Details and Free Trial of Self-Study Products at anaprep.com
YouTube Channel: karishma.anaprep
Travelling till end of May. Unable to respond timely till then!
Re: Find the range of values of x that satisfy the inequality (x - 3)^2
[#permalink]
14 Jul 2023, 09:12
14 Jul 2023, 09:12
1
Kudos
Expert Reply
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
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.
To read all our articles: Must read articles to reach Q51
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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ANA PREP BLOG, Private Tutoring Details and Free Trial of Self-Study Products at anaprep.com
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Travelling till end of May. Unable to respond timely till then!
ANA PREP BLOG, Private Tutoring Details and Free Trial of Self-Study Products at anaprep.com
YouTube Channel: karishma.anaprep
Travelling till end of May. Unable to respond timely till then!
gmatclubot
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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