BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

|2x + 3| > |7x - 2|

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760
by sanju09 » Tue Feb 24, 2009 4:26 am
What range of values of x will satisfy the inequality |2x + 3| > |7x - 2|?

A. x < (-1/9) or x > 5

B. -1 < x < (1/9)

C. (-1/9) < x < 1

D. (-1/9) < x < 5

E. x < (-1/9) or x > 1
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Site Admin
Posts: 2567
Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members
Thanked: 712 times
GMAT Score:770

by DanaJ » Tue Feb 24, 2009 5:24 am
Break it down into pieces, after noticing that |2x + 3| > |7x - 2| is equivalent to |2x + 3| - |7x - 2| > 0.
a. x is smaller than -3/2 then you get that:
|2x + 3| = -2x - 3
|7x - 2| = 2 - 7x
This means that the initial equation is equivalent to:
5x - 5 > 0 or 5x > 5 or x > 5. This is inconsistent with x < -3/2

b. x is between -3/2 and 2/7. You have:
|2x + 3| = 2x + 3
|7x - 2| = 2 - 7x
Initial equation will be:
9x + 1 > 0 or x > -1/9. So for this one the solution will be (-1/9, 2/7]

c. x is greater than 2/7. You get:
|2x + 3| = 2x + 3
|7x - 2| = 7x - 2
Initial euqation:
-5x + 5 > 0 or -5x > -5 or x < 1. Solution: (2/7, 1)


Put it all together and you get -1/9 < x < 1.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 319
Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members
Location: Delhi
Thanked: 84 times

Re: |2x + 3| > |7x - 2|

by sureshbala » Tue Feb 24, 2009 5:29 am
sanju09 wrote:What range of values of x will satisfy the inequality |2x + 3| > |7x - 2|?

A. x < (-1/9) or x > 5

B. -1 < x < (1/9)

C. (-1/9) < x < 1

D. (-1/9) < x < 5

E. x < (-1/9) or x > 1
A quick way is to eliminate the options....

Clearly, 0 satisfies the given expression.
So choices A and E are out.

1 does not satisfy the equation.
So choice D is out.

1/2 satisfies the equation.
So choice B is out.

Hence C is the answer
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 29
Joined: Sun Feb 08, 2009 11:29 am
Thanked: 3 times

Re: |2x + 3| > |7x - 2|

by ven4gmat » Tue Feb 24, 2009 5:46 am
sureshbala wrote:
sanju09 wrote:What range of values of x will satisfy the inequality |2x + 3| > |7x - 2|?

A. x < (-1/9) or x > 5

B. -1 < x < (1/9)

C. (-1/9) < x < 1

D. (-1/9) < x < 5

E. x < (-1/9) or x > 1
A quick way is to eliminate the options....

Clearly, 0 satisfies the given expression.
So choices A and E are out.

1 does not satisfy the equation.
So choice D is out.

1/2 satisfies the equation.
So choice B is out.

Hence C is the answer
One day I must get to this way of handling GMAT Quant...and the day is not so far if i stick to BTG
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 71
Joined: Sat Sep 20, 2008 5:48 am
Thanked: 5 times

by willbeatthegmat » Tue Feb 24, 2009 6:16 am
these kinda quest tortures me.....can someone tell me the technique to tackle such questions?????????

Thanks...
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 258
Joined: Thu Aug 07, 2008 5:32 am
Thanked: 16 times

Re: |2x + 3| > |7x - 2|

by x2suresh » Tue Feb 24, 2009 12:35 pm
My approach is similar to Suresh Bala's approach.


x=2 satisfies give equation.

eliminate A,D,E

x=1/2 eliminate B.

C is the answer
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Wed Aug 13, 2008 2:21 am
Thanked: 1 times

Re: |2x + 3| > |7x - 2|

by sudi760mba » Tue Feb 24, 2009 1:28 pm
sanju09 wrote:What range of values of x will satisfy the inequality |2x + 3| > |7x - 2|?

A. x < (-1/9) or x > 5

B. -1 < x < (1/9)

C. (-1/9) < x < 1

D. (-1/9) < x < 5

E. x < (-1/9) or x > 1
I'm going to take a stab at it and would like some validation:

2x + 3 > 7x - 2
=-5x > -5
= x< 1

The only one that seems to work is C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

Re: |2x + 3| > |7x - 2|

by sanju09 » Wed Feb 25, 2009 1:51 am
sudi760mba wrote:
sanju09 wrote:What range of values of x will satisfy the inequality |2x + 3| > |7x - 2|?

A. x < (-1/9) or x > 5

B. -1 < x < (1/9)

C. (-1/9) < x < 1

D. (-1/9) < x < 5

E. x < (-1/9) or x > 1
I'm going to take a stab at it and would like some validation:

2x + 3 > 7x - 2
=-5x > -5
= x< 1

The only one that seems to work is C.
More than one of the given choices could lead you to wonder that x < 1 works for those too. Yours is not a holistic treatment of the problem :) stab at its heart now :lol:
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1