Author 
Message 
TAGS:

Hide Tags

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1066
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
02 Nov 2012, 09:12
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: 453
Concentration: Marketing, Finance
GPA: 3.23

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
06 Dec 2012, 03:59
Answer: 3 <= x <= 7/5 More detailed solution for similar problems: http://burnoutorbreathe.blogspot.com/2012/12/howtogetsolutionforabsolutevalues.html
_________________
Impossible is nothing to God.



Intern
Joined: 24 Apr 2012
Posts: 48

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
18 Dec 2012, 01:33
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
TURN ON YOUR MINDS!!!



Retired Moderator
Joined: 05 Jul 2006
Posts: 1741

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
12 May 2013, 06:41
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 :
/3x2/ = /2x5/, thus 2 scenarios either 3x2 = 2x5 thus x = 7/5 or 3x2 = (2x5) 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 /3x2/ = /2x5/ , when u do this u ll end up with 3<=x<=7/5
Hope this helps



Director
Joined: 10 Mar 2013
Posts: 581
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
22 Oct 2015, 11:54
Bunuel wrote: GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
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. \(x<\frac{2}{3}\) > \(3x+2\leq2x+5\) > \(3\leq{x}\), as \(x<\frac{2}{3}\), then \(3\leq{x}<\frac{2}{3}\); B. \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) > \(3x2\leq2x+5\) > \(x\leq\frac{7}{5}\), as \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) , then \(\frac{2}{3}\leq{x}\leq\frac{7}{5}\); C. \(x>\frac{5}{2}\) > \(3x2\leq2x5\) > \(x\leq{3}\), 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.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
22 Oct 2015, 12:08
BrainLab wrote: Bunuel wrote: GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
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. \(x<\frac{2}{3}\) > \(3x+2\leq2x+5\) > \(3\leq{x}\), as \(x<\frac{2}{3}\), then \(3\leq{x}<\frac{2}{3}\); B. \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) > \(3x2\leq2x+5\) > \(x\leq\frac{7}{5}\), as \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) , then \(\frac{2}{3}\leq{x}\leq\frac{7}{5}\); C. \(x>\frac{5}{2}\) > \(3x2\leq2x5\) > \(x\leq{3}\), 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. Let me try to answer. For case A, we are assuming that x<2/3 . This condition alongwith the solution of x \(\geq\)3, gives the total range as \(2/3 > x \geq3\). Hope this helps.



Director
Joined: 10 Mar 2013
Posts: 581
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
22 Oct 2015, 12:47
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.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Director
Joined: 10 Mar 2013
Posts: 581
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
23 Oct 2015, 02:24
Let me try to answer. For case A, we are assuming that x<2/3 . This condition alongwith the solution of x \(\geq\)3, gives the total range as \(2/3 > x \geq3\). 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.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
23 Oct 2015, 04:36
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 3x2<=2x5 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 x34x8xhowmanysolutionsdoestheequation148996.html#p1193962The 2nd inequality does not have any solutions. Hope this helps.



Director
Joined: 10 Mar 2013
Posts: 581
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
17 Dec 2015, 04:44
GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
One way to solve is to square both the terms of course , but what is other way of solving it. Hi dear math experts, I'm just trying to find an approach that I understand and can apply for such kind of questions. If we have something like the expression below, we can just test 2 cases and it's a valid approach for this type. 2x  1 = 4x + 9 Solution: \(x =\frac{4}{3} or5\) \(2x1=4x+9\) or \(2x1=(4x+9)\) Both solutions satisfy this equation but as we saw in the example of Hussain15 it's not enough to solve absolute value inequalities . I think the most important point is here not to change the sign of an inequality and just expand the the absolute values . I've tried to solve it this way taking the approach from Hussain15 into sonsideration: We have 4 cases:Case 1: \(3x2 ≤ 2x5, x ≤ 3\) Case 2: \(3x2 ≤ 2x+5, x ≤ \frac{7}{5}\) Case 3: \(3x2 ≤ 2x5, x ≥ \frac{7}{5}\) Case 4: \(3x+2 ≤ 2x+5, x ≥ 3\) After inserting the values from the above ranges in the expression one can see that the expression hold true ONLY in Cases 4 and 2 \(−3≤x≤\frac{7}{5}\). The second important point I've observed here is that while testing 4 cases we see a pattern  we have actually 2 different values with the interchanginng inequality signs. Would it be a valid approach speaking generally about such kind of questions ? (Offcourse I'll try it out myself while solving other inequalities, but I don't have this experience yet)
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
17 Dec 2015, 06:12
BrainLab wrote: GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
One way to solve is to square both the terms of course , but what is other way of solving it. Hi dear math experts, I'm just trying to find an approach that I understand and can apply for such kind of questions. If we have something like the expression below, we can just test 2 cases and it's a valid approach for this type. 2x  1 = 4x + 9 Solution: \(x =\frac{4}{3} or5\) \(2x1=4x+9\) or \(2x1=(4x+9)\) Both solutions satisfy this equation but as we saw in the example of Hussain15 it's not enough to solve absolute value inequalities . I think the most important point is here not to change the sign of an inequality and just expand the the absolute values . I've tried to solve it this way taking the approach from Hussain15 into sonsideration: We have 4 cases:Case 1: \(3x2 ≤ 2x5, x ≤ 3\) Case 2: \(3x2 ≤ 2x+5, x ≤ \frac{7}{5}\) Case 3: \(3x2 ≤ 2x5, x ≥ \frac{7}{5}\) Case 4: \(3x+2 ≤ 2x+5, x ≥ 3\) After inserting the values from the above ranges in the expression one can see that the expression hold true ONLY in Cases 4 and 2 \(−3≤x≤\frac{7}{5}\). The second important point I've observed here is that while testing 4 cases we see a pattern  we have actually 2 different values with the interchanginng inequality signs. Would it be a valid approach speaking generally about such kind of questions ? (Offcourse I'll try it out myself while solving other inequalities, but I don't have this experience yet) Your method seems to be fine, I will mention mine below. But as GMAT questions comes with options, I would say that you also need to use the options to your favor in such questions. This question is asking for different discrete values or range of x. Your method is similar to the one mentioned below but is more time consuming. You can clearly see that with 2 of the 5 options as 1) 3<x<5 2)1<x<5 1 of these options can be eliminated by looking at x=2. Coming back to the analytical way to solve such questions, you are asked about the range of values of x satisfying 3x2<=2x5. Bunuel has mentioned the most straightforward solution at whatisthesolutionsetfor3x22x89266.html#p675126You need to look at 3 intervals : \(x<2/3\), \(2/3 \leq x < 5/2\) and \(x \geq 5/2\). Out of the above 3 intervals, the last one will give you no solution while the ranges from 1 and 2 will give you the desired solution of \(−3≤x≤\frac{7}{5}\)



Current Student
Joined: 22 Sep 2016
Posts: 207
Location: India
GPA: 4

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
13 Jul 2017, 20:39
GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
One way to solve is to square both the terms of course , but what is other way of solving it. How do we solve using square? (Sorry, I am sort of confused.) Would greatly appreciate, if you could please brief it once.
_________________
Desperately need 'KUDOS' !!



Manager
Status: GMAT...one last time for good!!
Joined: 10 Jul 2012
Posts: 71
Location: India
Concentration: General Management
GPA: 3.5

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
13 Jul 2017, 23:31
rekhabishop wrote: GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
One way to solve is to square both the terms of course , but what is other way of solving it. How do we solve using square? (Sorry, I am sort of confused.) Would greatly appreciate, if you could please brief it once. One more way to solve: (3x2)^2<=(2x5)^2 (3x2)^2(2x5)^2<=0 a2b2=(a+b)(ab) similarily (x+3)(5x7)<=0 two solutions: x=3,x=7/5 Now on a number line plot 3 and 7/5. Everything to extreme right mark '+' and alternate between them. ___+___(3)______________(7/5)__________+__________ We are looking for the equation to be less than or equal to zero. 3<=x<=7/5 is the solution
_________________
Kudos for a correct solution



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 274

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
26 Jul 2017, 04:50
Bunuel wrote: GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
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. \(x<\frac{2}{3}\) > \(3x+2\leq2x+5\) > \(3\leq{x}\), as \(x<\frac{2}{3}\), then \(3\leq{x}<\frac{2}{3}\); B. \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) > \(3x2\leq2x+5\) > \(x\leq\frac{7}{5}\), as \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) , then \(\frac{2}{3}\leq{x}\leq\frac{7}{5}\); C. \(x>\frac{5}{2}\) > \(3x2\leq2x5\) > \(x\leq{3}\), as \(x>\frac{5}{2}\), then in this range we have no solution; Ranges from A and B give us the solution as: \(3\leq{x}\leq\frac{7}{5}\). excellent ..! very didactic post ...



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 274

Re: What is the solution set for 3x2<=2x5 [#permalink]
Show Tags
29 Jul 2017, 04:00
Bunuel wrote: GMATMadeeasy wrote: What is the solution set for \(3x2\leq2x5\)
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. \(x<\frac{2}{3}\) > \(3x+2\leq2x+5\) > \(3\leq{x}\), as \(x<\frac{2}{3}\), then \(3\leq{x}<\frac{2}{3}\); B. \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) > \(3x2\leq2x+5\) > \(x\leq\frac{7}{5}\), as \(\frac{2}{3}\leq{x}\leq\frac{5}{2}\) , then \(\frac{2}{3}\leq{x}\leq\frac{7}{5}\); C. \(x>\frac{5}{2}\) > \(3x2\leq2x5\) > \(x\leq{3}\), 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 when evaluating between 2/3 and 7/5, you have selected 7/5, and when evaluating between 3 and 2/3, you have selected 3 as the range for final solution... Is this because, you have already set the range of x, as x is less than 2/3 for condition A, and have set the range of x, as x is less than 5/2 and greater than 2/3 for condition B, or you have taken the help of number line when setting the range for final solution that is "x is greater than or equal to 3 and smaller than or equal to 7/5" please shed some light on this issue ... thanks in advance




Re: What is the solution set for 3x2<=2x5
[#permalink]
29 Jul 2017, 04:00



Go to page
Previous
1 2
[ 35 posts ]



