It is currently 22 Sep 2017, 04:53

### 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

# Find the solution set for the following inequality -2|3-2x|

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Feb 2012
Posts: 47

Kudos [?]: 64 [2], given: 14

Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

14 Mar 2012, 12:42
2
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

67% (00:59) correct 33% (01:25) wrong based on 68 sessions

### HideShow timer Statistics

Hi everybody,

can please s.o. help me with this question?

Many thanks

Find the solution set for the following inequality -2|3-2x| < 14?

Kudos [?]: 64 [2], given: 14

Math Expert
Joined: 02 Sep 2009
Posts: 41683

Kudos [?]: 124408 [4], given: 12078

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

14 Mar 2012, 13:03
4
KUDOS
Expert's post
6
This post was
BOOKMARKED
NYC5648 wrote:
Hi everybody,

can please s.o. help me with this question?

Many thanks

Find the solution set for the following inequality -2|3-2x| < 14?

Is it: $$-2*|3-2x|<14$$? If yes, then $$-2*|3-2x|=negative*nonnegative=nonpositive$$, which is ALWAYS less than positive number 14. So this inequality holds true for any $$x$$.
_________________

Kudos [?]: 124408 [4], given: 12078

Math Expert
Joined: 02 Sep 2009
Posts: 41683

Kudos [?]: 124408 [3], given: 12078

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

16 Mar 2012, 04:27
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
shankar245 wrote:
Hi Buneul,
Why cant we do as we do normally as in
take a positive solution , then a negative solution?

x<5
x>-2

What am i doing wrong here?

If you do it properly you'll get the same answer. But you don't need that.

Consider this: $$-2*|3-2x|<14$$ --> reduce by negative -2 and flip the sign: $$|3-2x|>-7$$ --> LHS is an absolute value, which is always nonnegative, so $$|3-2x|$$ will always be more than negative -7, so it'll be more for all values of $$x$$.

Hope it's clear.
_________________

Kudos [?]: 124408 [3], given: 12078

Math Expert
Joined: 02 Sep 2009
Posts: 41683

Kudos [?]: 124408 [1], given: 12078

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

15 Mar 2012, 01:48
1
KUDOS
Expert's post
optimisttageja wrote:
|3-2x| can have two possible solns, either it is (3-2x) or -(3-2x) so wr can solve this ques as

-2*(3-2x)<14 => x<5
or
-2*-(3-2x)<14 => x>-4

combining above two

-4
is the solution.

Posted from my mobile device

Sometimes it's a good idea to check whether your solution is correct by plug-in method. So, plug x=10 or x=-10 and see whether the inequality holds true.

Refer for the correct solution above.

Hope it helps.
_________________

Kudos [?]: 124408 [1], given: 12078

Math Expert
Joined: 02 Sep 2009
Posts: 41683

Kudos [?]: 124408 [1], given: 12078

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

17 Mar 2012, 07:53
1
KUDOS
Expert's post
BN1989 wrote:
I have a general question.

If I have an inequality with an absolute value expression, why can't I simplify the absolute value expression.

First I can devide by -2, which gives me |3-2x|>-7

Now why can't I check the two cases for the absolute value expression that I have to check when absolute value expression are in equalities?

Please read my responses above: YOU DO NOT NEED TO DO THAT, since LHS is an absolute value then it's ALWAYS more than negative number -7, so it'll be more for ALL values of x.
_________________

Kudos [?]: 124408 [1], given: 12078

Intern
Joined: 16 Feb 2012
Posts: 3

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

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

15 Mar 2012, 01:41
|3-2x| can have two possible solns, either it is (3-2x) or -(3-2x) so wr can solve this ques as

-2*(3-2x)<14 => x<5
or
-2*-(3-2x)<14 => x>-4

combining above two

-4is the solution.

Posted from my mobile device
_________________

its never funny the second time

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

Intern
Joined: 16 Feb 2012
Posts: 3

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

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

15 Mar 2012, 02:16
Yes i guess my soln was wrong.. x could take values -infinity to infinity..

Posted from my mobile device
_________________

its never funny the second time

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

Manager
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 109

Kudos [?]: 13 [0], given: 19

Concentration: Strategy, General Management
GMAT 1: 460 Q35 V20
GPA: 3.6
WE: Consulting (Computer Software)
Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

15 Mar 2012, 12:33
Hi Buneul,
Why cant we do as we do normally as in
take a positive solution , then a negative solution?

x<5
x>-2

What am i doing wrong here?

Kudos [?]: 13 [0], given: 19

Manager
Joined: 12 Oct 2011
Posts: 131

Kudos [?]: 247 [0], given: 23

GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

17 Mar 2012, 06:45
I have a general question.

If I have an inequality with an absolute value expression, why can't I simplify the absolute value expression.

First I can devide by -2, which gives me |3-2x|>-7

Now why can't I check the two cases for the absolute value expression that I have to check when absolute value expression are in equalities?

Kudos [?]: 247 [0], given: 23

Senior Manager
Joined: 13 Aug 2012
Posts: 462

Kudos [?]: 526 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

05 Dec 2012, 03:08
-2|3-2x| < 14
|3-2x| > -7

What value of x will satisfy the equation? Any value since |3 - 2x| is always positive no matter what value of x.
_________________

Impossible is nothing to God.

Kudos [?]: 526 [0], given: 11

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17594

Kudos [?]: 270 [0], given: 0

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

05 Nov 2014, 08:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 270 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17594

Kudos [?]: 270 [0], given: 0

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

26 Nov 2015, 00:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 270 [0], given: 0

Intern
Joined: 24 Oct 2015
Posts: 1

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

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

23 Jan 2016, 05:29
umm, i get -2<x<5

-2|3-2x|<14

solution 1
-2*(3-2x)< 14
-6+4x<14
4x<14+6
4x<20
x<5

solution 2
-2*-1(3-2x)<14
6-4x<14
6-14<4x
-8<4x
-2<x

-2<x<5

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

Manager
Joined: 27 Aug 2016
Posts: 95

Kudos [?]: 4 [0], given: 149

Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
GPA: 3
WE: Engineering (Energy and Utilities)
Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

25 Dec 2016, 08:50
Bunuel wrote:
BN1989 wrote:
I have a general question.

If I have an inequality with an absolute value expression, why can't I simplify the absolute value expression.

First I can devide by -2, which gives me |3-2x|>-7

Now why can't I check the two cases for the absolute value expression that I have to check when absolute value expression are in equalities?

Please read my responses above: YOU DO NOT NEED TO DO THAT, since LHS is an absolute value then it's ALWAYS more than negative number -7, so it'll be more for ALL values of x.

Thanx Bunuel...your solution is well understood...but i guess lot of people are asking why do we not get the same answer may be something like x=negative infinity to positive infinity if we solve it through conventional and probably lengthier process...as in the rush of things (timer etc) the "QUALITATIVE ASSESSMENT" may or may not click in mind...thanx..pl help.

Kudos [?]: 4 [0], given: 149

Intern
Joined: 04 Sep 2016
Posts: 2

Kudos [?]: 1 [0], given: 3

Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

### Show Tags

21 Jan 2017, 18:19
Quote:
BN1989 wrote:
I have a general question.

If I have an inequality with an absolute value expression, why can't I simplify the absolute value expression.

First I can devide by -2, which gives me |3-2x|>-7

Now why can't I check the two cases for the absolute value expression that I have to check when absolute value expression are in equalities?

Please read my responses above: YOU DO NOT NEED TO DO THAT, since LHS is an absolute value then it's ALWAYS more than negative number -7, so it'll be more for ALL values of x.

I understand the reason why we dont need to do the lengthy process since LHS is an absolute value. Since this topic is difficult for me I try to solve with the longer way just to get more grasp of the concept.

If we get the solutions graphically it comes out as -2 < x < 5. But it should have come for any value of x. What am i doing wrong?

The range i have got is by simplifying -2|3-2x| < 14 in the following way
|3-2x| > 7
=| -2 (x-3/2) | > 7
=2 |x-3/2| > 7
=|x-3/2 | > 7/2

Kudos [?]: 1 [0], given: 3

Re: Find the solution set for the following inequality -2|3-2x|   [#permalink] 21 Jan 2017, 18:19
Similar topics Replies Last post
Similar
Topics:
29 Which of the following inequalities has a solution set, when graphed 12 20 Mar 2016, 02:14
41 Which of the following inequalities has a solution set that 9 21 Dec 2016, 22:24
44 Which of the following inequalities has a solution set that 12 30 Jul 2017, 06:21
49 Which of the following inequalities has a solution set, when 17 15 Aug 2017, 13:34
7 Which of the following inequalities has a solution set that, 9 20 Sep 2014, 16:55
Display posts from previous: Sort by