Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Nov 2015, 15:10

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the solution set for |3x-2|<=|2x-5|

Author Message
TAGS:
Current Student
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1095
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 34

Kudos [?]: 396 [0], given: 69

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  02 Nov 2012, 08:12
Thanx i just needed to clarify it is just by substitution of a value from the range that you decide the sign with which inequality should be multiplied.
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 18

Kudos [?]: 309 [0], given: 11

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  06 Dec 2012, 02:59
Answer: -3 <= x <= 7/5

More detailed solution for similar problems: http://burnoutorbreathe.blogspot.com/2012/12/how-to-get-solution-for-absolute-values.html
_________________

Impossible is nothing to God.

Manager
Joined: 24 Mar 2010
Posts: 81
Followers: 0

Kudos [?]: 35 [0], given: 134

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  16 Dec 2012, 21:43
Bunuel,

I used some of my knowledge gained through one of your posts. - which-of-the-following-represents-the-complete-range-of-x-108884.html

and rephrased the question as

|3x-2|- |2x-5| <= 0

Critical Points , x = 2/3 , 5/2

Checked the sign for an extreme value ( x = 1000) and got it as positive. Then just alternated the signs and got the range as

2/3<x<5/2 will be the range for x <0

Where am I going wrong?
_________________

- Stay Hungry, stay Foolish -

Math Expert
Joined: 02 Sep 2009
Posts: 30377
Followers: 5091

Kudos [?]: 57335 [0], given: 8811

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  16 Dec 2012, 22:04
Expert's post
eaakbari wrote:
Bunuel,

I used some of my knowledge gained through one of your posts. - which-of-the-following-represents-the-complete-range-of-x-108884.html

and rephrased the question as

|3x-2|- |2x-5| <= 0

Critical Points , x = 2/3 , 5/2

Checked the sign for an extreme value ( x = 1000) and got it as positive. Then just alternated the signs and got the range as

2/3<x<5/2 will be the range for x <0

Where am I going wrong?

Check here: what-is-the-solution-set-for-3x-2-2x-89266.html#p675126
_________________
Intern
Joined: 24 Apr 2012
Posts: 48
Followers: 0

Kudos [?]: 20 [0], given: 1

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  18 Dec 2012, 00:33
Ans:
to solve this we see that there are 4 cases, when both are –ve, both +ve, and alternately –ve and +ve..therefore we get the solution set as -3<equal to x<equal 7/5.
_________________

www.mnemoniceducation.com

SVP
Joined: 05 Jul 2006
Posts: 1513
Followers: 5

Kudos [?]: 164 [0], given: 39

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  12 May 2013, 05:41
In addition to the critical points that each absolute value expression has ( 2/3 and 5/2) there is another 2 critical points that comes from their interaction together that are ( 2/3 and 7/5) those last 2 critical points you can get by equating the 2 absolute values :

/3x-2/ = /2x-5/, thus 2 scenarios either 3x-2 = 2x-5 thus x = 7/5 or 3x-2 = -(2x-5) thus x = -3

you then draw the number line as follows

......-3..........2/3........7/5..............5/2...............

you then test each region by substituting values from each region into the original inequality /3x-2/ = /2x-5/ , when u do this u ll end up with -3<=x<=7/5

Hope this helps
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 7290
Followers: 384

Kudos [?]: 93 [0], given: 0

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  08 Oct 2014, 21:51
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.
_________________
Senior Manager
Joined: 10 Mar 2013
Posts: 436
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT Date: 05-27-2015
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 3

Kudos [?]: 67 [0], given: 197

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  22 Oct 2015, 10:54
Bunuel wrote:
What is the solution set for $$|3x-2|\leq|2x-5|$$

One way to solve is to square both the terms of course , but what is other way of solving it.

First you should determine the check points (key points): $$\frac{2}{3}$$ and $$\frac{5}{2}$$. Hence we'll have three ranges to check:

A. $$x<\frac{2}{3}$$ --> $$-3x+2\leq-2x+5$$ --> $$-3\leq{x}$$, as $$x<\frac{2}{3}$$, then $$-3\leq{x}<\frac{2}{3}$$;

B. $$\frac{2}{3}\leq{x}\leq\frac{5}{2}$$ --> $$3x-2\leq-2x+5$$ --> -$$x\leq\frac{7}{5}$$, as $$\frac{2}{3}\leq{x}\leq\frac{5}{2}$$ , then $$\frac{2}{3}\leq{x}\leq\frac{7}{5}$$;

C. $$x>\frac{5}{2}$$ --> $$3x-2\leq2x-5$$ --> $$x\leq{-3}$$, as $$x>\frac{5}{2}$$, then in this range we have no solution;

Ranges from A and B give us the solution as: $$-3\leq{x}\leq\frac{7}{5}$$.

Hi Bunuel, I've one question regarding your solution. I'm using the same method as you...

A. $$-3\leq{x}$$ can be <2/3 and >2/3 how do you limit the range of first expression $$-3\leq{x}$$ ? -2 ok, 100 not... or we can just say by the soltion x=3 and is in the given range x>2/3.
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 1634
GMAT 1: 650 Q49 V30
GMAT 2: 690 Q49 V34
GMAT 3: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 45

Kudos [?]: 614 [0], given: 367

What is the solution set for |3x-2|<=|2x-5| [#permalink]  22 Oct 2015, 11:08
BrainLab wrote:
Bunuel wrote:
What is the solution set for $$|3x-2|\leq|2x-5|$$

One way to solve is to square both the terms of course , but what is other way of solving it.

First you should determine the check points (key points): $$\frac{2}{3}$$ and $$\frac{5}{2}$$. Hence we'll have three ranges to check:

A. $$x<\frac{2}{3}$$ --> $$-3x+2\leq-2x+5$$ --> $$-3\leq{x}$$, as $$x<\frac{2}{3}$$, then $$-3\leq{x}<\frac{2}{3}$$;

B. $$\frac{2}{3}\leq{x}\leq\frac{5}{2}$$ --> $$3x-2\leq-2x+5$$ --> -$$x\leq\frac{7}{5}$$, as $$\frac{2}{3}\leq{x}\leq\frac{5}{2}$$ , then $$\frac{2}{3}\leq{x}\leq\frac{7}{5}$$;

C. $$x>\frac{5}{2}$$ --> $$3x-2\leq2x-5$$ --> $$x\leq{-3}$$, as $$x>\frac{5}{2}$$, then in this range we have no solution;

Ranges from A and B give us the solution as: $$-3\leq{x}\leq\frac{7}{5}$$.

Hi Bunuel, I've one question regarding your solution. I'm using the same method as you...

A. $$-3\leq{x}$$ can be <2/3 and >2/3 how do you limit the range of first expression $$-3\leq{x}$$ ? -2 ok, 100 not... or we can just say by the soltion x=3 and is in the given range x>2/3.

For case A, we are assuming that x<2/3 . This condition alongwith the solution of x $$\geq$$-3, gives the total range as $$2/3 > x \geq-3$$.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Senior Manager
Joined: 10 Mar 2013
Posts: 436
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT Date: 05-27-2015
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 3

Kudos [?]: 67 [0], given: 197

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  22 Oct 2015, 11:47
Thanks Engr2012, I think I've mixed it up with such kind of questions, where we have clear roots....

|x+3|−|4−x|=|8+x|. How many solutions does the equation have?

Solution: There are 3 key points here: -8, -3, 4. So we have 4 conditions:
a) x<−8. −(x+3)−(4−x)=−(8+x) --> x=−1 is not within that range and so not valid
b) −8≤x<−3. −(x+3)−(4−x)=(8+x) --> x=−15 is not within that range and so not valid
c) −3≤x<4. (x+3)−(4−x)=(8+x) --> x=9 is not within that range and so not valid
d) x≥4. (x+3)+(4−x)=(8+x) --> x=−1 is not within that range and so not valid
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Senior Manager
Joined: 10 Mar 2013
Posts: 436
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT Date: 05-27-2015
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 3

Kudos [?]: 67 [0], given: 197

Re: What is the solution set for |3x-2|<=|2x-5| [#permalink]  23 Oct 2015, 01:24

For case A, we are assuming that x<2/3 . This condition alongwith the solution of x $$\geq$$-3, gives the total range as $$2/3 > x \geq-3$$.

Hope this helps.[/quote]

Hi Engr2012, I've one more question; If we would have been asked to find not the ranges but the solutions for this example.. what would be the eanswer here ? Or by such kind of inequalities we are talking always about ranges like 0<x<5 and not x=5
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 1634
GMAT 1: 650 Q49 V30
GMAT 2: 690 Q49 V34
GMAT 3: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 45

Kudos [?]: 614 [0], given: 367

What is the solution set for |3x-2|<=|2x-5| [#permalink]  23 Oct 2015, 03:36
BrainLab wrote:
Hi Engr2012, I've one more question; If we would have been asked to find not the ranges but the solutions for this example.. what would be the eanswer here ? Or by such kind of inequalities we are talking always about ranges like 0<x<5 and not x=5

What example are you talking about? Is it the question |3x-2|<=|2x-5| or |x+3|−|4−x|=|8+x| ? If it is 1st, then your question is not clear. It is an inequality and as such needs to have a range (often) of values. As for the 2nd example, refer to x-3-4-x-8-x-how-many-solutions-does-the-equation-148996.html#p1193962

The 2nd inequality does not have any solutions.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

What is the solution set for |3x-2|<=|2x-5|   [#permalink] 23 Oct 2015, 03:36

Go to page   Previous    1   2   [ 32 posts ]

Similar topics Replies Last post
Similar
Topics:
If 3^{(x+2)}-3^{x}=6^{3}(3^{7}), what is the value of x? 0 03 Sep 2015, 00:35
5 If (x + 4)(3x + 1) = 3x^2 + x, what is a possible value of x? 5 31 Aug 2015, 09:42
1 Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis 2 12 May 2015, 10:51
7 If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value 3 06 Nov 2014, 07:56
1 If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y? 2 28 Mar 2010, 08:32
Display posts from previous: Sort by