Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

inequalities

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Legendary Member
Posts: 789
Joined: Sun May 06, 2007 1:25 amFollowed by: 6 members
Location: Southern California, USA
Thanked: 15 times
by resilient » Thu Apr 03, 2008 7:54 pm
How many possible integer values are there for x, if Absolute value 4x-3 <6?

a.1
b.2
c3
d4
e5


fairly simple question when set up this way:

-6 <4x-3<6 this will drive to the correct answer..


however, my initial approach was wrong and I would like to know why?

pos: 4x-3<6 = x< 9/4

neg: 4x-3<-6 = x<-3/4

thus, both answer give infinite negative digits? what went wrong?
Appetite for 700 and I scraped my plate!
Top
Join the discussion
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3224
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

Re: inequalities

by Stuart@KaplanGMAT » Thu Apr 03, 2008 8:47 pm
Enginpasa1 wrote:How many possible integer values are there for x, if Absolute value 4x-3 <6?

a.1
b.2
c3
d4
e5


fairly simple question when set up this way:

-6 <4x-3<6 this will drive to the correct answer..


however, my initial approach was wrong and I would like to know why?

pos: 4x-3<6 = x< 9/4

neg: 4x-3<-6 = x<-3/4

thus, both answer give infinite negative digits? what went wrong?
The problem is that you divided by a negative and didn't realize it.

The two solutions are actually:

+(4x-3) < 6

and

-(4x-3) < 6

and when we "move" the negative sign over in the second inequality, we're really multiplying both sides by -1, which reverses the inequality.

So, the second inequality becomes:

4x -3 > -6
4x > -3
x > -(3/4)
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Legendary Member
Posts: 789
Joined: Sun May 06, 2007 1:25 amFollowed by: 6 members
Location: Southern California, USA
Thanked: 15 times

I get it

by resilient » Thu Apr 03, 2008 10:19 pm
Crystal Clear. Now I understand! WHat method should I employ in order to never repeat the problem again?
Appetite for 700 and I scraped my plate!
Top
Join the discussion
User avatar
GMAT Instructor
Posts: 3224
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

Re: I get it

by Stuart@KaplanGMAT » Fri Apr 04, 2008 9:44 am
Enginpasa1 wrote:Crystal Clear. Now I understand! WHat method should I employ in order to never repeat the problem again?
Whenever you see absolute value and inequalities, be very careful. Also, whenever you "cancel out" or "move over" a number, be aware that what you're really doing is dividing or multiplying both sides of the equation (or inequality) by that number. Especially when inequalities are involved, doing so can have unexpected consequences.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Senior | Next Rank: 100 Posts
Posts: 55
Joined: Sun Apr 06, 2008 5:04 pm

by sampleresume » Sun Apr 06, 2008 5:15 pm
The answer is five. X can be any value of -2, -1, 0, 1, and 2.
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 188
Joined: Sun Dec 23, 2007 7:40 am
Location: INDIA
Thanked: 4 times

by senthil » Mon Apr 07, 2008 1:52 am
could you please explain me why have we taken this inequality...
-6 <4x-3<6 .....


Thanks
Senthil
Top
Join the discussion
Legendary Member
Posts: 789
Joined: Sun May 06, 2007 1:25 amFollowed by: 6 members
Location: Southern California, USA
Thanked: 15 times

by resilient » Mon Apr 07, 2008 8:36 am
Senthil:

we start with this in absolute form: 4x-3 <6 SO whenever we see absolutes we need to worry about the pos and neg outcome.

pos:
4x-3<6

neg: -4x+3>6 (> since we are charging the whole situation by negative.) This changes the sign. After that, we come to your final solution. I hope that helps
Appetite for 700 and I scraped my plate!
Top
Join the discussion
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Mon Mar 31, 2008 6:09 pm

by GMAT_crusher » Mon Apr 07, 2008 7:08 pm
Still missing something here
checking for -6 < 4x-3 < 6

x for (4x - 3)
1 = 1
2 = 5
0 = -3

3 = 9
-1 = -7
-2 = -11
-3 = -16

total x values fit is 3!! what am I missing!!!
Top
Join the discussion
Legendary Member
Posts: 789
Joined: Sun May 06, 2007 1:25 amFollowed by: 6 members
Location: Southern California, USA
Thanked: 15 times

ok

by resilient » Mon Apr 07, 2008 7:36 pm
the golden rule to understand is to know that with absolutes you need to account for a positive outcome and negative outcome. On top of this you need to make sure that whenver you divide by a negative you have to change the sign of the inequality! I suggest you read up a bit on inequalities and absolutes. Try to fullyunderstand and synthesize Stuarts explanation!
Appetite for 700 and I scraped my plate!
Top
Join the discussion
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Wed Feb 20, 2008 7:15 pmFollowed by: 1 member
Thanked: 6 times

by mmukher » Mon Apr 07, 2008 7:47 pm
Still missing something here
checking for -6 < 4x-3 < 6

x for (4x - 3)
1 = 1
2 = 5
0 = -3

3 = 9
-1 = -7
-2 = -11
-3 = -16

total x values fit is 3!! what am I missing!!!

you were almost there. The question states that x is an integer, so you need to ignore 0.

The actual answer was never stated clearly. Its B.

-3/4 < x < 2.5 so x can be 1,2 (not 0)
Top
Join the discussion
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Fri Oct 12, 2007 1:29 am

by sandeepdeb » Tue Apr 08, 2008 1:11 am
Can anyone please tell the corretc answer? I though 0 is an integer and the answer to this question is 3. X lies between -3/4 and 9/4 and so, the possible integer values are 0,1 and 2.
Top
Join the discussion
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Wed Feb 20, 2008 7:15 pmFollowed by: 1 member
Thanked: 6 times

by mmukher » Tue Apr 08, 2008 7:53 am
My Bad. 0 is an integer. Possible values are 0,1,2 Answer is C.3
Top
Join the discussion