x^4+4


Close

Bạn đang xem: x^4+4

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 đồ sộ Daily Prep Questions via tin nhắn.

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 đồ sộ your email? No problem, unsubscribe here.

Hello Guest!

It appears that you are browsing the GMAT Club diễn đàn unregistered!

Signing up is free, quick, and confidential.
Join 700,000+ members and get the full benefits of GMAT Club

Registration gives you:

  • Tests

    Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan Prep. All are không tính phí for GMAT Club members.

  • Applicant Stats

    View detailed applicant stats such as GPA, GMAT score, work experience, location, application status, and more

  • Books/Downloads

    Download thousands of study notes, question collections, GMAT Club’s Grammar and Math books. All are free!

and many more benefits!

  • Jan 10

    770 on the GMAT? It's a goal that many students aspire đồ sộ achieve, but only 1% of all test takers receive it. Watch this interview đồ sộ learn how Mantavya scored a remarkable 770 GMAT with just 2 months of preparation in first attempt.

  • Jan 11

    1. GMAT Club Tests Are Focus Ready: Now Featuring 5 Full Length Focus Tests: 2. Why You Should Use LSAT Tests for GMAT RC & CR: 3. From 650 on GMAT Classic đồ sộ 695 (98th Percentile) on GMAT Focus: and more.

  • Jan 13

    Do you want đồ sộ ace the GMAT Focus? Join Piyush Beriwala in this webinar as he guides you through a smart study plan đồ sộ achieve the 99th %ile on the GMAT Focus. Learn the best strategies and tips đồ sộ master the test and boost your score.

  • Jan 13

    Attend this session đồ sộ learn how đồ sộ Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.

  • Jan 13

    Attend this không tính phí GMAT Algebra Webinar and learn how đồ sộ master the most challenging Inequalities and Absolute Value problems with ease.

  • Jan 13

    2000+ không tính phí GMAT videos | 20+ tiện ích help videos | 15+ interview prep videos

  • Jan 15

    András Domschitz recently scored 735 (99.5%) on the GMAT Focus Edition. In this Clip, we discuss his GMAT Focus study plan and techniques and how TTP’s self-study course helped him achieve an incredible 735 score on the GMAT Edition

  • Jan 15

    Video explanations + diagnosis of 10 weakest areas + one-week access đồ sộ 10 SC e-books and 200 short videos!

  • Jan 16

    Join Giorgio and many other students who have used Target Test Prep đồ sộ score high on the GMAT Focus Edition. Start your 5-day trial of the TTP GMAT Course today for FREE.

User avatar

Intern

Intern

Joined: 09 Apr 2012

Posts: 48

When is |x - 4| = 4 - x? [#permalink] New post  03 May 2012, 10:38

Question Stats:

59% (01:07) correct 41% (01:01) wrong based on 2821 sessions

Hide Show timer Statistics

When is |x - 4| = 4 - x?

A. x = 4
B. x = 0
C. x > 4
D. x <= 4
E. x < 0

Math Expert

Joined: 02 Sep 2009

Posts: 90831

Re: When is |x - 4| = 4 - x? [#permalink] New post  03 May 2012, 11:04

nkimidi7y wrote:

When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how tự i prove this using algebra?

Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) đồ sộ be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.
_________________

User avatar

Current Student

Joined: 23 Oct 2010

Posts: 238

Location: Azerbaijan

Concentration: Finance

Re: When is |x - 4| = 4 - x? [#permalink] New post  08 May 2012, 09:57

nkimidi7y wrote:

4-x is always >=0.
So x is always <=4.

Is this what you have meant?

|x-4| = 4-x

1) |x-4| is ALWAYS none negative.
so , 4-x must be also more or equal đồ sộ zero

4-x>=0
x<=4

2) if x<4 , then 4-x=4-x
if x>=4 x-4=4-x x=4

so x <= 4
_________________

Happy are those who dream dreams and are ready đồ sộ pay the price đồ sộ make them come true

I am still on all gmat forums. msg u if you want đồ sộ ask u smth

User avatar

Intern

Intern

Joined: 09 Apr 2012

Posts: 48

Re: When is |x - 4| = 4 - x? [#permalink] New post  03 May 2012, 14:00

4-x is always >=0.
So x is always <=4.

Is this what you have meant?

avatar

Intern

Intern

Joined: 12 Dec 2011

Posts: 7

Location: Italy

Concentration: Finance, Entrepreneurship

GMAT Date: 04-09-2013

GPA: 4

WE:Management Consulting (Consulting)

Re: When is |x - 4| = 4 - x? [#permalink] New post  28 Oct 2012, 01:56

Bunuel wrote:

nkimidi7y wrote:

When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how tự i prove this using algebra?

Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) đồ sộ be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.

Hi Bunuel
I am trying đồ sộ understand theese two properties, but how is it possible đồ sộ have |X|=-X, in order that absolute value has đồ sộ be always positive?
Could you please provide u an explaination in more details?
Thanks in advance

Math Expert

Joined: 02 Sep 2009

Posts: 90831

Re: When is |x - 4| = 4 - x? [#permalink] New post  29 Oct 2012, 01:56

mario1987 wrote:

Bunuel wrote:

nkimidi7y wrote:

When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how tự i prove this using algebra?

Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). For example: \(|5|=5\);

So, \(|x-4|=4-x=-(x-4)\) đồ sộ be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).

Answer: D.

Hope it's clear.

Hi Bunuel
I am trying đồ sộ understand theese two properties, but how is it possible đồ sộ have |X|=-X, in order that absolute value has đồ sộ be always positive?
Could you please provide u an explaination in more details?
Thanks in advance

When \(x\leq{0}\), for example when \(x=-5\), then \(|-5|=5=-(-5)\) sánh \(|x|=-x\) (|negative |=-(negative)=positive).

For more kiểm tra Absolute Value chapter of Math book:

math-absolute-value-modulus-86462.html

Hope it helps.
_________________

User avatar

Senior Manager

Senior Manager

Joined: 13 Aug 2012

Posts: 337

Concentration: Marketing, Finance

GPA: 3.23

Re: When is |x - 4| = 4 - x? [#permalink] New post  05 Dec 2012, 03:51

|x-4| = 4-x

Absolute values are always positive or greater kêu ca 0.
So, 4-x >= 0 ==> x <= 4

Answer: D

There is no need đồ sộ test values.

avatar

Intern

Intern

Joined: 27 Nov 2012

Status:Need some help

Posts: 8

Location: United States

Concentration: General Management, Human Resources

GPA: 3.56

WE:Sales (Internet and New Media)

Re: When is |x - 4| = 4 - x? [#permalink] New post  06 Jan 2013, 13:26

Hi brunel,

You said some expression when it is > = 0 then l some espression l <= some expression.

In this case how tự i know X-4 is >= 0

Thanks!

Math Expert

Joined: 02 Sep 2009

Posts: 90831

Re: When is |x - 4| = 4 - x? [#permalink] New post  07 Jan 2013, 02:37

LiquidGrave wrote:

Hi brunel,

You said some expression when it is > = 0 then l some espression l <= some expression.

In this case how tự i know X-4 is >= 0

Thanks!

We have that \(|x-4|=4-x=-(x-4)\). So, \(|some \ expression|\leq{-(some \ expression)}\), thus \(x-4\leq{0}\) --> \(x\leq{4}\).

Hope it's clear.
_________________

avatar

Intern

Intern

Joined: 08 Feb 2013

Posts: 1

Re: When is |x - 4| = 4 - x? [#permalink] New post  10 Feb 2013, 05:14

Why not E?

If i am not mistaken when x<0, then |x-1| = x-1?

Math Expert

Joined: 02 Sep 2009

Posts: 90831

Re: When is |x - 4| = 4 - x? [#permalink] New post  10 Feb 2013, 05:21

Victorlp89 wrote:

Why not E?

If i am not mistaken when x<0, then |x-1| = x-1?

First of all we have |x-4| = 4-x not |x-1| = x-1.

Next, |x-1| = x-1 for \(x\geq{1}\).

If \(x\leq{1}\), then \(|x-1|=-(x-1)=1-x\)
_________________

User avatar

Intern

Intern

Joined: 05 Mar 2013

Posts: 13

Re: When is |x - 4| = 4 - x? [#permalink] New post  13 Mar 2013, 13:45

how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand

User avatar

Manager

Manager

Joined: 24 Sep 2012

Posts: 68

Location: United States

Concentration: Entrepreneurship, International Business

GPA: 3.2

WE:Education (Education)

Re: When is |x - 4| = 4 - x? [#permalink] New post  14 Mar 2013, 12:19

Absolute value of any number or expression must be positive.
If (x-4) is positive then |x-4| is also positive
What if x-4 is negative? Since the absolute value must be positive, |x-4| would be equal đồ sộ -(x-4)=4-x.
Right?

We know that x-4 would have đồ sộ be negative for the equation in question đồ sộ be true. This would imply that x would have đồ sộ be a small positive number smaller kêu ca 4 or a negative number. You can take examples đồ sộ test that.
x=-14 (x-4)=-ve
x=1, x-4=-3 -ve
x=4, implies x-4=0 and 4-x=0. Thus, the equation is satisfied.

Hence, d is the answer.

Coming đồ sộ your question, if a question đơn hàng with equality it also indirectly đơn hàng with inequality. If you say the equation is satisfied when x=0,x=4,x=-5 and sánh on, it also implies that the equation is true for all values of x less kêu ca or equal đồ sộ 4.

An equation exists only at certain points. We have đồ sộ find those points and if those points range over a large space, the easiest way would be express it as inequality.

Note: An equality question can have answers which might be expressed as inequalities. There is nothing wrong with it.

Hope it helps! Let u know if I can help you any further.

dhlee922 wrote:

how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand

User avatar

Intern

Intern

Joined: 05 Mar 2013

Posts: 13

Re: When is |x - 4| = 4 - x? [#permalink] New post  14 Mar 2013, 16:34

thanks Kris. that does help. i guess my follow up question would be, is there a way đồ sộ solve it algebraically rather kêu ca plugging in numbers?

Kris01 wrote:

Absolute value of any number or expression must be positive.
If (x-4) is positive then |x-4| is also positive
What if x-4 is negative? Since the absolute value must be positive, |x-4| would be equal đồ sộ -(x-4)=4-x.
Right?

We know that x-4 would have đồ sộ be negative for the equation in question đồ sộ be true. This would imply that x would have đồ sộ be a small positive number smaller kêu ca 4 or a negative number. You can take examples đồ sộ test that.
x=-14 (x-4)=-ve
x=1, x-4=-3 -ve
x=4, implies x-4=0 and 4-x=0. Thus, the equation is satisfied.

Hence, d is the answer.

Coming đồ sộ your question, if a question đơn hàng with equality it also indirectly đơn hàng with inequality. If you say the equation is satisfied when x=0,x=4,x=-5 and sánh on, it also implies that the equation is true for all values of x less kêu ca or equal đồ sộ 4.

An equation exists only at certain points. We have đồ sộ find those points and if those points range over a large space, the easiest way would be express it as inequality.

Note: An equality question can have answers which might be expressed as inequalities. There is nothing wrong with it.

Hope it helps! Let u know if I can help you any further.

dhlee922 wrote:

how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand

User avatar

Manager

Manager

Joined: 24 Jan 2013

Posts: 62

Re: When is |x - 4| = 4 - x? [#permalink] New post  14 Mar 2013, 17:19

When is |x-4| = 4-x?

Critical Values method:

The Critical Value here is x=4 (we make the absolute value term equal đồ sộ zero), sánh we have this conditions đồ sộ check:

1) x<4: -(x-4)=4-x ---> x-4=x-4 ---> true for all values of x, but only when x<4 the initial condition is satisfied ---> true always that x<4

2) x=4: 0=0 ---> this is true always that x=4

3) x>4: x-4=4-x ---> 2x=8 ---> x=4 ---> initial condition of x>4 is not met

Therefore, there is a solution only when: x<=4

Solution D

User avatar

Manager

Manager

Joined: 24 Sep 2012

Posts: 68

Location: United States

Concentration: Entrepreneurship, International Business

GPA: 3.2

WE:Education (Education)

Re: When is |x - 4| = 4 - x? [#permalink] New post  15 Mar 2013, 10:26

As Johnwesley said, for |x-4|=4-x, s-4 should be negative or equal đồ sộ 0.

i.e. x-4<=0
Hence, x<=4

[quote="dhlee922"]thanks Kris. that does help. i guess my follow up question would be, is there a way đồ sộ solve it algebraically rather kêu ca plugging in numbers?

User avatar

Intern

Intern

Joined: 01 Sep 2012

Status:Joining Cranfield Sep 2014

Posts: 42

Concentration: Technology, General Management

GMAT 1: 530 Q50 V14

GMAT 2: 630 Q48 V29

WE:Engineering (Energy and Utilities)

Re: When is |x - 4| = 4 - x? [#permalink] New post  09 Aug 2013, 21:24

I solved it in this way.

When is |x-4| = 4-x?

Choice A: X=4, it is true but X cannot be always 4
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>4, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=4, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is D.

It took only 1min đồ sộ solve this problem with above method.

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

User avatar

VP

VP

Joined: 06 Sep 2013

Posts: 1355

Concentration: Finance

Re: When is |x - 4| = 4 - x? [#permalink] New post  19 Dec 2013, 04:14

Bunuel wrote:

Victorlp89 wrote:

Why not E?

If i am not mistaken when x<0, then |x-1| = x-1?

First of all we have |x-4| = 4-x not |x-1| = x-1.

Next, |x-1| = x-1 for \(x\geq{1}\).

If \(x\leq{1}\), then \(|x-1|=-(x-1)=1-x\)

Hi Bunuel,

Sinetunes you can manipulate say |x-4|=|-(-x+4)|=|4-x| is what you'll kết thúc up with.

So then how tự you solve when you have |4-x| = 4-x?

Is this property correct or what are its limitations?

Thanks
J :)

Math Expert

Joined: 02 Sep 2009

Posts: 90831

Re: When is |x - 4| = 4 - x? [#permalink] New post  19 Dec 2013, 04:32

jlgdr wrote:

Bunuel wrote:

Victorlp89 wrote:

Why not E?

If i am not mistaken when x<0, then |x-1| = x-1?

First of all we have |x-4| = 4-x not |x-1| = x-1.

Next, |x-1| = x-1 for \(x\geq{1}\).

If \(x\leq{1}\), then \(|x-1|=-(x-1)=1-x\)

Hi Bunuel,

Sinetunes you can manipulate say |x-4|=|-(-x+4)|=|4-x| is what you'll kết thúc up with.

So then how tự you solve when you have |4-x| = 4-x?

Is this property correct or what are its limitations?

Thanks
J :)

\(|4-x| = 4-x\) --> \(4-x\geq{0}\) --> \(x\leq{4}\).
_________________

User avatar

VP

VP

Joined: 06 Sep 2013

Posts: 1355

Concentration: Finance

Re: When is |x - 4| = 4 - x? [#permalink] New post  19 Dec 2013, 05:54

Silly u, thats correct
Thanks
Cheers
J:)

Posted from my mobile device

Re: When is |x - 4| = 4 - x? [#permalink]

19 Dec 2013, 05:54

Moderators:

Xem thêm: tourism is a big business

Senior Moderator - Masters Forum

3139 posts

cron