Last visit was: 22 Apr 2026, 10:30 It is currently 22 Apr 2026, 10:30
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,747
Own Kudos:
810,636
 [42]
Given Kudos: 105,820
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,747
Kudos: 810,636
 [42]
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 05 May 2016, 00:57
1
Kudos
Add Kudos
41
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

76% (02:22) correct 24% (02:40) wrong based on 840 sessions

History

Date
Time
Result
Not Attempted Yet
In the equation |6x+9| = |3x+25|, what is the sum of all possible values of x?

A. 4/9
B. 4/5
C. 14/9
D. 15/7
E. 17/3
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
sashiim20
User avatar
Joined: 04 Dec 2015
Last visit: 05 Jun 2024
Posts: 608
Own Kudos:
1,972
 [47]
Given Kudos: 276
Location: India
Concentration: Technology, Strategy
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
Posts: 608
Kudos: 1,972
 [47]
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 05 May 2016, 06:32
41
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Hello...
I followed the Absolute value equation Strategies... got answer c - 14/9

Following is the explanation:

We need to test four cases overall: positive/positive, positive/negative, negative/positive, and negative/negative.
(1) The positive/positive case: (6x+9) = (3x+25)
(2) The positive/negative case: (6x+9) = -(3x+25)
(3) The negative/positive case: —(6x+9) = (3x+25)
(4) The negative/negative case: —(6x+9) = -(3x+25)

case (1) and case (4) yield the same equation. Likewise, case (2) and case (3) yield the same equation. Thus only need to consider two real cases: one in which neither expression changes sign, and another in which one expression changes sign.

CASE A: Same sign
6x+9 = 3x+25
6x-3x = 25-9
3x = 16
x=16/3

CASE B: Different Sign
-(6x+9) = (3x+25)
-6x-9 = 3x+25
-6x-3x=25+9
-9x=34
x=-34/9

Sum of all possible values of x = 16/3+(-34/9)
16/3-34/9 = 14/9 (Answer C) :-D

Please, consider giving kudos if you find my answer helpful in any way :) :good :thumbup:
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
44,993
 [28]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 44,993
 [28]
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 05 May 2016, 03:43
13
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
Bunuel
In the equation |6x+9| = |3x+25|, what is the sum of all possible values of x?

A. 4/9
B. 4/5
C. 14/9
D. 15/7
E. 17/3
Show more

since it is MOD on both sides we can square both sides..
thereafter we get the two terms on ONE side and we will have a QUADRATIC equation..
In a Quadratic equation, the value of sum of roots /x is\(-\frac{(coeff of x}{coeff of x^2)}\)..
so lets concentrate ONLY on x^2 and x values..

\(|6x+9| = |3x+25|\)..
\((6x+9)^2 = (3x+25)^2\)..
\(36x^2 +108 x+ 9^2 = 9x^2+150x +25^2\)..
\((36-9)x^2 + (108-150)x +9^2+25^2\)..
sum of the roots =\(\frac{-b}{a} = -(\frac{-42}{27}) = \frac{14}{9}\)
C
General Discussion
User avatar
Skywalker18
User avatar
Retired Moderator
Joined: 08 Dec 2013
Last visit: 15 Nov 2023
Posts: 1,973
Own Kudos:
10,161
Given Kudos: 171
Status:Greatness begins beyond your comfort zone
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Products:
My Reviews
Posts: 1,973
Kudos: 10,161
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 05 May 2016, 03:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x<-25/3
- 6x - 9 = -3x - 25
=> 3x = 16
=> x = 16/3

-25/3 < x < -9/6
6x + 9 = -(3x+25)
=> 6x+9 = -3x - 25
=> 9x = -34
=> x = -34/9

x> -9/6
6x+9 = 3x+25
=> 3x = 16
=> x = 16/3

Sum of all possible values of a = 16/3 + (-34/9)
=48/9 - 34/9
=14/9

Answer C
User avatar
Anurag06
User avatar
Joined: 10 Dec 2019
Last visit: 23 Mar 2020
Posts: 40
Own Kudos:
6
Given Kudos: 15
Posts: 40
Kudos: 6
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 06 Feb 2020, 06:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Skywalker18
x<-25/3
- 6x - 9 = -3x - 25
=> 3x = 16
=> x = 16/3

-25/3 < x < -9/6
6x + 9 = -(3x+25)
=> 6x+9 = -3x - 25
=> 9x = -34
=> x = -34/9

x> -9/6
6x+9 = 3x+25
=> 3x = 16
=> x = 16/3

Sum of all possible values of a = 16/3 + (-34/9)
=48/9 - 34/9
=14/9

Answer C
Show more

Hi

I added all 3 values and ended up getting 16/3 + 16/3 - 16/9
which resulted in to 80/9.

Probably it could be silly mistake from my end but can you please help me out here?
avatar
NHiromoto
avatar
Current Student
Joined: 22 Jun 2019
Last visit: 17 Apr 2022
Posts: 6
Own Kudos:
23
 [1]
Given Kudos: 22
Location: Japan
Schools: INSEAD Aug 22 intake (A)
Schools: INSEAD Aug 22 intake (A)
Posts: 6
Kudos: 23
 [1]
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 21 Mar 2020, 03:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Anurag06
Skywalker18
x<-25/3
- 6x - 9 = -3x - 25
=> 3x = 16
=> x = 16/3

-25/3 < x < -9/6
6x + 9 = -(3x+25)
=> 6x+9 = -3x - 25
=> 9x = -34
=> x = -34/9

x> -9/6
6x+9 = 3x+25
=> 3x = 16
=> x = 16/3

Sum of all possible values of a = 16/3 + (-34/9)
=48/9 - 34/9
=14/9

Answer C

Hi

I added all 3 values and ended up getting 16/3 + 16/3 - 16/9
which resulted in to 80/9.

Probably it could be silly mistake from my end but can you please help me out here?
Show more

Anurag06
When x<-25/3, x = 16/3 is not possible.
So, you should add 2 values(16/3 and -34/9) only
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 22 Apr 2026
Posts: 8,627
Own Kudos:
5,190
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,627
Kudos: 5,190
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 16 Aug 2020, 08:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In the equation |6x+9| = |3x+25|, what is the sum of all possible values of x?

A. 4/9
B. 4/5
C. 14/9
D. 15/7
E. 17/3
Show more

for given eqn |6x+9| = |3x+25l
the possible values of x
6x+9 = 3x+25
x=16/3 and
6x+9=-3x-25
x=-34/9
its sum l
16/3-34/9 ; 14/9
OPTION C
User avatar
Target4bschool
User avatar
Joined: 29 Dec 2019
Last visit: 20 Jan 2026
Posts: 57
Own Kudos:
64
Given Kudos: 181
Schools: IE MiM (Sep 21 Start) (A)
Schools: IE MiM (Sep 21 Start) (A)
Posts: 57
Kudos: 64
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 25 Aug 2020, 06:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
Bunuel
In the equation |6x+9| = |3x+25|, what is the sum of all possible values of x?

A. 4/9
B. 4/5
C. 14/9
D. 15/7
E. 17/3

since it is MOD on both sides we can square both sides..
thereafter we get the two terms on ONE side and we will have a QUADRATIC equation..
In a Quadratic equation, the value of sum of roots /x is\(-\frac{(coeff of x}{coeff of x^2)}\)..
so lets concentrate ONLY on x^2 and x values..

\(|6x+9| = |3x+25|\)..
\((6x+9)^2 = (3x+25)^2\)..
\(36x^2 +108 x+ 9^2 = 9x^2+150x +25^2\)..
\((36-9)x^2 + (108-150)x +9^2+25^2\)..
sum of the roots =\(\frac{-b}{a} = -(\frac{-42}{27}) = \frac{14}{9}\)
C
Show more

Please correct me if I am wrong.
Though the answer is correct but the approach may be wrong as squaring produces more roots, which may not be same as of the original equation.
Here, it is mod, I think that's why it produced the same result.
avatar
dep
avatar
Joined: 23 Feb 2018
Last visit: 07 Aug 2021
Posts: 82
Own Kudos:
119
Given Kudos: 23
Posts: 82
Kudos: 119
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 21 Sep 2020, 08:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|6x+9| = |3x+25|

\((6x+9)^2 = (3x+25)^2\)

\((6x+9)^2 - (3x+25)^2 = 0\)

(6x+9+3x+25) (6x+9 -3x-25) =0

(9x+ 34)(3x-16) = 0

x = \(\frac{-34}{9}\) or \(\frac{16}{3}\)

sum = \(\frac{16}{3}-(\frac{-34}{9})\) =\(\frac{14}{9}\)
IMO C
avatar
huzaifahirani
avatar
Joined: 23 Jul 2020
Last visit: 24 Feb 2022
Posts: 3
Own Kudos:
4
Given Kudos: 59
Posts: 3
Kudos: 4
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 21 Sep 2020, 13:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|6x+9| = |3x+25|
(6x+9)^2 –(3x+25)^2 = 0
Hint Difference of squares: a2 – b2 = (a + b)(a – b)
(6x+9+3x+25)( 6x+9-3x-25) = 0
Solve for x
(9x+34)(3x-16) = 0
X = -34/9 & X2 = 16/3
Sum of x is
(-34/9) + (16/3)
((3)(-34)+(9)(16)) / ((9)(3))
Sum = 14/9

Hope this helps!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,967
Own Kudos:
1,117
Posts: 38,967
Kudos: 1,117
In the equation |6x+9| = |3x+25|, what is the sum of all possible valu 08 Jun 2025, 10:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109747 posts
Krunaal
Tuck School Moderator
853 posts