NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 00:47 It is currently 26 Apr 2024, 00:47
Decision Tracker
My Rewards
New posts
New comers' posts

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

Inequalities+absolute value

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Own Kudos [?]: 194 [1]
Given Kudos: 275
Inequalities+absolute value [#permalink] New post   10 Jun 2017, 22:02
1
Kudos
Hello all

I have a confusion in inequalities and absolute value questions.
For example,

|2x-4|<6

So we have two possibilities:

2x-4<6
x<5

And

2x-4>-6
2x>-2
x>-1

So the range of values of x is: -1<x<5


But my questions is that why don't we take this in the second scenario:

-(2x-4)>6 (I took this because we know that the number inside the modes can be negative or positive)

But this gives us: -2x+4>6

-2x>2
x<-1 this is totally opposite of the previous answer.


Can anyone please explain this because I am not able to understand what exactly is going wrong?


Also one more query:

| x-5| >7

Means that distance of x from 5 on the number line is greater than 7.

Can this be true for this as well?

|x+5|>7



Please help!!

Thanks
User avatar
L
abhimahna
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3600
Own Kudos [?]: 5426 [2]
Given Kudos: 346
Send PM
Reviews Badge
Inequalities+absolute value [#permalink] New post   10 Jun 2017, 22:17
2
Kudos
Expert Reply
Hi Shiv2016,

Ideally |x| = x if x>0
= -x if x<0

Now looking at your 1st question,

|2x-4|<6

Here |2x-4| can be written as either 2x-4 or -(2x-4)

So, when I take these values in the original question, I will get

2x-4<6 or -(2x-4)<6

=> 2x < 10 or -2x + 4 < 6

=> x<5 or -x < 1

=> x<5 or x > -1

Hence, -1<x<5 is the solution.

Now your 2nd query:

| x-5| >7 => Means that distance of x from 5 on the number line is greater than 7. -- CORRECT (Here, we have 5 as the zero point.)

|x+5|>7 => Can this be true for this as well? -- INCORRECT. Here, we have -5 as the zero point. So, it should be distance of x from -5 on the number line is greater than 7

I would suggest, read the following post to get proper clarity on modulus concept.

https://gmatclub.com/forum/math-absolut ... 86462.html
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Own Kudos [?]: 194 [1]
Given Kudos: 275
Re: Inequalities+absolute value [#permalink] New post   11 Jun 2017, 22:04
1
Kudos
abhimahna wrote:
Shiv2016 wrote:
I will surely go through the absolute value post you have mentioned.

One quick question:
When you considered: -(2x-4)<6

Why did we not reverse the sign because now its negative on left hand side?


We reverse the sign only when we multiply the inequality by a negative sign.

You see I wrote -2x + 4 < 6 then I solved it as -x < 1.

Now since I need x instead of -x , I multiplied the inequlity with -1, hence the sign of the inequality was reversed and we got x > -1.

I hope it makes sense. :)


Hi abhimahna

I have the same doubt as I am not able to really understand it after going through various posts and the link you told me about.

|2x-4|<6

It means that the positive value of 2x-4 is less than 6. It means that distance of 2x from 4 is less than 6.

But when we write: -2x+4<6

I am still confused as to why we do not change the sign. This doubt persists because absolute value= positive value and thus the sign would remain the same but when we take the negative value on L.H.S, we are multiplying it by negative 1. And when we multiply or divide by negative 1 we change the sign.

If you don't mind, can you please explain this (below) on a number line so that I understand what exactly is going on here.

|x-4|<6

Means distance of x from 4 is less than 6.

|x+4|<6

Does this also means the same or +/- change how we read this expression?


Looking forward to your reply.

Thanks
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Own Kudos [?]: 194 [0]
Given Kudos: 275
Re: Inequalities+absolute value [#permalink] New post   10 Jun 2017, 22:28
abhimahna wrote:
Hi Shiv2016,

Ideally |x| = x if x>0
= -x if x<0

Now looking at your 1st question,

|2x-4|<6

Here |2x-4| can be written as either 2x-4 or -(2x-4)

So, when I take these values in the original question, I will get

2x-4<6 or -(2x-4)<6

=> 2x < 10 or -2x + 4 < 6

=> x<5 or -x < 1

=> x<5 or x > -1

Hence, -1<x<5 is the solution.

Now your 2nd query:

| x-5| >7 => Means that distance of x from 5 on the number line is greater than 7. -- CORRECT (Here, we have 5 as the zero point.)

|x+5|>7 => Can this be true for this as well? -- INCORRECT. Here, we have -5 as the zero point. So, it should be distance of x from -5 on the number line is greater than 7

I would suggest, read the following post to get proper clarity on modulus concept.

https://gmatclub.com/forum/math-absolut ... 86462.html



I will surely go through the absolute value post you have mentioned.

One quick question:
When you considered: -(2x-4)<6

Why did we not reverse the sign because now its negative on left hand side?
User avatar
L
abhimahna
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3600
Own Kudos [?]: 5426 [0]
Given Kudos: 346
Send PM
Reviews Badge
Re: Inequalities+absolute value [#permalink] New post   10 Jun 2017, 22:35
Expert Reply
Shiv2016 wrote:
I will surely go through the absolute value post you have mentioned.

One quick question:
When you considered: -(2x-4)<6

Why did we not reverse the sign because now its negative on left hand side?


We reverse the sign only when we multiply the inequality by a negative sign.

You see I wrote -2x + 4 < 6 then I solved it as -x < 1.

Now since I need x instead of -x , I multiplied the inequlity with -1, hence the sign of the inequality was reversed and we got x > -1.

I hope it makes sense. :)
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Own Kudos [?]: 194 [0]
Given Kudos: 275
Re: Inequalities+absolute value [#permalink] New post   10 Jun 2017, 23:12
abhimahna wrote:
Shiv2016 wrote:
I will surely go through the absolute value post you have mentioned.

One quick question:
When you considered: -(2x-4)<6

Why did we not reverse the sign because now its negative on left hand side?


We reverse the sign only when we multiply the inequality by a negative sign.

You see I wrote -2x + 4 < 6 then I solved it as -x < 1.

Now since I need x instead of -x , I multiplied the inequlity with -1, hence the sign of the inequality was reversed and we got x > -1.

I hope it makes sense. :)


So in this case, we are not multiplying it by -1 but it is already in that form i.e. positive and negative.

Thanks for you reply.
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Own Kudos [?]: 194 [0]
Given Kudos: 275
Re: Inequalities+absolute value [#permalink] New post   10 Jun 2017, 23:14
If we read the expression, it means (according to me) that absolute value (i.e. the positive value) of 2x-4 is less than 6.
But when we read the second version, it means that the negative absolute value of -2x+4 is less than 6.


Is it sounding weird or its fine?
User avatar
L
abhimahna
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3600
Own Kudos [?]: 5426 [0]
Given Kudos: 346
Send PM
Reviews Badge
Re: Inequalities+absolute value [#permalink] New post   10 Jun 2017, 23:18
Expert Reply
Shiv2016 wrote:
If we read the expression, it means (according to me) that absolute value (i.e. the positive value) of 2x-4 is less than 6.
But when we read the second version, it means that the negative absolute value of -2x+4 is less than 6.


Is it sounding weird or its fine?


yes, that is true. This is how we read it and everything sounds cool. :)
avatar
G
Shiv2016
Director
Director
Joined: 02 Sep 2016
Posts: 528
Own Kudos [?]: 194 [0]
Given Kudos: 275
Re: Inequalities+absolute value [#permalink] New post   10 Jun 2017, 23:25
abhimahna wrote:
Shiv2016 wrote:
If we read the expression, it means (according to me) that absolute value (i.e. the positive value) of 2x-4 is less than 6.
But when we read the second version, it means that the negative absolute value of -2x+4 is less than 6.


Is it sounding weird or its fine?


yes, that is true. This is how we read it and everything sounds cool. :)



That's great. Thanks so much for your reply. Because i have read everywhere that ABSOLUTE VALUE can never be negative, that is what caused me trouble in understanding inequalities+absolute value of an expression.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32679
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: Inequalities+absolute value [#permalink] New post   11 Jun 2021, 23:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
GMAT Club Bot
gmatclubot
Re: Inequalities+absolute value [#permalink]
11 Jun 2021, 23:28
Moderator:
Bunuel
Math Expert
92918 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions