Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 May 2016, 02:47
GMAT Club Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

aboslute value inequalities

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 25 Jul 2005
Posts: 48
Followers: 0

Kudos [?]: 4 [0], given: 0

aboslute value inequalities [#permalink]

Show Tags

New post 23 Oct 2005, 10:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

|3x-2|<=|2x-5|

Hi,
Can someone let me know if there's another approach to solve this problem besides squaring both sides to remove the absolute value inequalities first?

Thanks.
Director
Director
avatar
Joined: 21 Aug 2005
Posts: 793
Followers: 2

Kudos [?]: 18 [0], given: 0

 [#permalink]

Show Tags

New post 23 Oct 2005, 10:38
If there is nothing mentioned about x, for x=0, this is false. For -ve integer values of x, it is true and for positive values it is true.
Can you please post the whole question?
Intern
Intern
avatar
Joined: 25 Jul 2005
Posts: 48
Followers: 0

Kudos [?]: 4 [0], given: 0

 [#permalink]

Show Tags

New post 23 Oct 2005, 11:02
gsr wrote:
If there is nothing mentioned about x, for x=0, this is false. For -ve integer values of x, it is true and for positive values it is true.
Can you please post the whole question?


This is the original question:
Find the solution set for the following inequalities |3x-2|<=|2x-5|

The first step of the explanatory answer for this question from 4gmat ebook is squaring both sides to get rid of the absolute value sign.
(3x-2)^2<=(2x-5)^2

However, I read once that
Quote:
"Another way to eliminate an absolute value is to square both sides of the equation. Taking the absolute value makes things non-negative, and squaring makes things non-negative. So, if you square something, you no longer need to take its absolute value. However, be careful when squaring both sides of an equation as this can lead to extraneous solutions."
from http://www.richland.edu/james/lecture/m116/prerequisites.html

Thus, I would like to know if there's an approach other than squaring both sides.

Let me know if you want to see the OE.
Manager
Manager
avatar
Joined: 05 Oct 2005
Posts: 81
Followers: 1

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

 [#permalink]

Show Tags

New post 24 Oct 2005, 10:41
Is the answer the following?

x <= 7/5
Manager
Manager
avatar
Joined: 05 Oct 2005
Posts: 81
Followers: 1

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

 [#permalink]

Show Tags

New post 24 Oct 2005, 10:57
For the record, I came up with x <= 7/5 by using the squaring method. Frankly, I think it's easier than trying to pick numbers to come up with an answer. For this problem, squaring is the much easier method.

|3x-2| <= |2x-5|
(3x-2)^2 <= (2X-5)^2
9x^2 - 12x + 4 <= 4x^2 - 20x + 25
5x^2 + 8x -21 <= 0
(5x-7)(x+3) <= 0
x <= -3 or 5x <= 7
x <= -3 or x <= 7/5

Because we know that x is <= either -3 or 7/5, take the larger number, 7/5.
Intern
Intern
avatar
Joined: 25 Jun 2005
Posts: 23
Location: Bay Area, CA
Followers: 0

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

 [#permalink]

Show Tags

New post 08 Nov 2005, 18:36
If you dont want to square both sides, then here is the other way, which is usually shorter, however, I found that it is lengthier/error prone for me for this question:

for x < 2/3 and x < 5/2 => x < 2/3
x >= 3

for x < 2/3 and x > 5/2
x >= 3/5

for x > 2/3 and x < 5/2 => 2/3 < x < 5/2
x <= 7/5

for x > 2/3 and x > 5/2 => x > 5/2
x <= -3

The only solution that is valid for range is x < 7/5 for 2/3 < x < 5/2
_________________

If you can't change the people, change the people.

  [#permalink] 08 Nov 2005, 18:36
Display posts from previous: Sort by

aboslute value inequalities

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.