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

 It is currently 22 May 2015, 23:33

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Inequality and absolute values

Author Message
TAGS:
Director
Joined: 28 Dec 2005
Posts: 758
Followers: 1

Kudos [?]: 8 [0], given: 0

Inequality and absolute values [#permalink]  25 Jun 2006, 16:08
This is possibly a repost.....but if possible could someone explain the right way to solve this?

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

The way I see it, we would end up with 4 possible equations:

3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)

Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment...
 Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes
Director
Joined: 16 Aug 2005
Posts: 946
Location: France
Followers: 1

Kudos [?]: 10 [0], given: 0

Re: Inequality and absolute values [#permalink]  25 Jun 2006, 16:20
Futuristic wrote:
This is possibly a repost.....but if possible could someone explain the right way to solve this?

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

The way I see it, we would end up with 4 possible equations:

3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)

Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment...

Since you have to consider 4 different scenarios for absolute value problems like this one above, squaring it and then solving is faster.
_________________

I believe its yogurt!

Director
Joined: 28 Dec 2005
Posts: 758
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: Inequality and absolute values [#permalink]  25 Jun 2006, 16:47
gmatmba wrote:
Futuristic wrote:
This is possibly a repost.....but if possible could someone explain the right way to solve this?

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

The way I see it, we would end up with 4 possible equations:

3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)

Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment...

Since you have to consider 4 different scenarios for absolute value problems like this one above, squaring it and then solving is faster.

I'm aware of the solution by squaring. Are we sure that it provides a solution with all possible values of x?
Senior Manager
Joined: 09 Mar 2006
Posts: 445
Followers: 1

Kudos [?]: 6 [0], given: 0

Re: Inequality and absolute values [#permalink]  25 Jun 2006, 21:11
Futuristic wrote:
gmatmba wrote:
Futuristic wrote:
This is possibly a repost.....but if possible could someone explain the right way to solve this?

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

The way I see it, we would end up with 4 possible equations:

3x -2 <= 2x - 5 ......(1)
3x -2 <= -2x + 5 ....(2)
-3x + 2 <= 2x -5 ....(3)
-3x +2 <= -2x + 5 ..(4)

Is the above correct? If so, I solved to get x <= 7/5, x>= -1, x <= 03, x >= 7/5. However, 4GMAT seems to solve this by squaring the absolute values on both sides of the equation....please comment...

Since you have to consider 4 different scenarios for absolute value problems like this one above, squaring it and then solving is faster.

I'm aware of the solution by squaring. Are we sure that it provides a solution with all possible values of x?

If you square absolute values, the final equation will have exactly the same roots as the original. However if some of the variables are not in absolute values, you can end up with more roots then the original (consider |x|=2x+1 ). But you will never lose a root because of squaring.
Director
Joined: 28 Dec 2005
Posts: 758
Followers: 1

Kudos [?]: 8 [0], given: 0

Great, thanks for confirming.
Similar topics Replies Last post
Similar
Topics:
Question about inequalities and absolute value? 2 21 Jan 2015, 19:19
2 Inequalities and Absolute value Question Bank 0 18 Sep 2013, 05:59
absolute value and inequality 9 07 Jul 2009, 16:06
1 Inequality involving absolute values 5 08 Nov 2007, 16:14
Another DS from GMATPrep -- Absolute Value Inequalities 7 10 May 2006, 14:31
Display posts from previous: Sort by