Last visit was: 31 Dec 2024, 05:50 It is currently 31 Dec 2024, 05:50
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

|4x+24|= 96

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30559
Own Kudos [?]: 36907 [4]
Given Kudos: 26113
Send PM
|4x+24|= 96 [#permalink] New post   25 Dec 2018, 16:46
1
Expert Reply
3
Bookmarks
00:00

Question Stats:

63% (01:06) correct 36% (00:56) wrong based on 182 sessions

Hide Show timer Statistics

\(|4x+24|= 96\)

\(|4x|=120\)

Quantity A
Quantity B
x
18


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
ShowHide Answer
Official Answer
B
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12239 [4]
Given Kudos: 136
Send PM

Top Member of the Month
Re: |4x+24|= 96 [#permalink] New post   27 Dec 2018, 09:07
3
1
Bookmarks
Carcass wrote:
\(|4x+24|= 96\)

\(|4x|=120\)

Quantity A
Quantity B
x
18



There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

GIVEN: |4x+24|= 96
So, EITHER 4x + 24 = 96 OR 4x + 24 = -96
If 4x + 24 = 96, then x = 18
If 4x + 24 = -96, then x = -30
Both x-values work upon testing

GIVEN: |4x|= 120
So, EITHER 4x = 120 OR 4x = -120
If 4x = 120, then x = 30
If 4x = -120, then x = -30
Both x-values work upon testing

IMPORTANT: Only ONE value (x = -30) satisfies BOTH equations, so x MUST equal -30

We get:
QUANTITY A: -30
QUANTITY B: 18

Answer: B

Cheers,
Brent
avatar
chetan2u
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Own Kudos [?]: 471 [0]
Given Kudos: 0
Send PM
Re: |4x+24|= 96 [#permalink] New post   27 Dec 2018, 22:23
Expert Reply
Carcass wrote:
\(|4x+24|= 96\)

\(|4x|=120\)

Quantity A
Quantity B
x
18


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



Hi..

Many ways..

(I) number line
Look at the problem from the number line view..
\(|4x+24|= 96\) means 4x is 96 units away from -24.
\(|4x|=120\) means 4x is 120 units away from 0.
Thus, 4x is closer to -24 than to 0. So 4x is negative and so is x.
A is negative and B is 18, so B>A.

(II) As both sides positive, square both sides.
\(|4x+24|= 96....|x+6|=24....x^2+12x+36=576....x^2+12x-540=0....(X+30)(x-18)=0\), so x is 18 or -30
\(|4x|=120.....|x|=30\), so x is 30 or -30..
Common is x is -30, so A is -30 and B is 18, so B>A.

(III) open the Modulus.
\(|4x+24|= 96\)
(a) 4x+24=96...4x=72...X=18
(b) 4x+24=-96...4x=-120...x=-30 AND
\(|4x|=120\)
(a) 4x=120...x=30
(b) 4x=-120...x=-30
Thus, x=-30 and B>A

B

More on modulus..
See the post in signature below
avatar
Fatemeh
Manager
Manager
Joined: 22 Feb 2018
Posts: 163
Own Kudos [?]: 215 [0]
Given Kudos: 0
Send PM
Re: |4x+24|= 96 [#permalink] New post   04 Jan 2019, 17:40
Answer: B

|4x+24| = 96
|4x| = 120

From second expression:
We have |4x| = 120 so:
Either 4x=120 or -4x =120, So:
Either x =30 or x=-30

From first expression:
We have |4x+24| = 96
Either 4x+24 = 96 or -(4x+24) = 96

Considering both expression, we should look which one makes sense:
If x =30 then 4x+24 = 144
If x =-30 then 4x+24 = 96

So x should be -30 and is less than B
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5090
Own Kudos [?]: 76 [0]
Given Kudos: 0
Send PM
Re: |4x+24|= 96 [#permalink] New post   30 Jul 2023, 11:09
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
gmatclubot
Re: |4x+24|= 96 [#permalink]
30 Jul 2023, 11:09
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1126 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact