[phpBB Debug] PHP Notice: in file /viewtopic.php on line 1525: Undefined array key "topic_tags_visibility"
[phpBB Debug] PHP Notice: in file /viewtopic.php on line 1526: Undefined array key "timer_statistics_visibility"
If |x + 1| = 2|x - 1|, what is the sum of the roots? : Multiple-choice Questions — Select One Answer Choice

Last visit was: 22 Jul 2024, 16:07 It is currently 22 Jul 2024, 16:07

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.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29147
Own Kudos [?]: 34186 [3]
Given Kudos: 25534
Send PM
Retired Moderator
Joined: 02 Dec 2020
Posts: 1833
Own Kudos [?]: 2133 [2]
Given Kudos: 140
GRE 1: Q168 V157

GRE 2: Q167 V161
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11874 [4]
Given Kudos: 136
Send PM
Manager
Manager
Joined: 11 Jan 2022
Posts: 72
Own Kudos [?]: 11 [0]
Given Kudos: 437
Send PM
Re: If |x + 1| = 2|x - 1|, what is the sum of the roots? [#permalink]
Does it work both ways? If I take 2|x-1|= +- |x+1| will I get the same answer?

GreenlightTestPrep wrote:
Carcass wrote:
If |x + 1| = 2|x - 1|, what is the sum of the roots?

A. 4
B. 6
C. 8
D. 20/3
E. 10/3


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book

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: |x+1|=2|x-1|

So, EITHER x+1=2(x-1) OR x+1=-[2(x-1)]

x+1=2(x-1)
Expand: x + 1 = 2x - 2
Solve: x = 3

x+1=-[2(x-1)]
Expand: x + 1 = -2x + 2
Solve: x = 1/3

When we plug the solutions into the original equation, we find that there are no extraneous roots

So, the SUM of the solutions = 3 + 1/3
= 3 1/3
= 10/3

Answer: E
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11874 [0]
Given Kudos: 136
Send PM
Re: If |x + 1| = 2|x - 1|, what is the sum of the roots? [#permalink]
Chaithraln2499 wrote:
Does it work both ways? If I take 2|x-1|= +- |x+1| will I get the same answer?


Yes it works both ways.

In general, we can write: If |x| = |y| then we must consider two options:
1) x = y
2) x = -y OR -x = y (both equations are considered equivalent, so it doesn't matter which one you choose to work with)
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4661
Own Kudos [?]: 69 [0]
Given Kudos: 0
Send PM
Re: If |x + 1| = 2|x - 1|, what is the sum of the roots? [#permalink]
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
Re: If |x + 1| = 2|x - 1|, what is the sum of the roots? [#permalink]
Moderators:
GRE Instructor
52 posts
GRE Forum Moderator
29 posts
Moderator
1093 posts
GRE Instructor
218 posts

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