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

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Re: What is the solution set for |3x-2|<=|2x-5| [#permalink] New post 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.
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Re: What is the solution set for |3x-2|<=|2x-5| [#permalink] New post 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
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Re: What is the solution set for |3x-2|<=|2x-5| [#permalink] New post 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?
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Re: What is the solution set for |3x-2|<=|2x-5| [#permalink] New post 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
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Re: What is the solution set for |3x-2|<=|2x-5| [#permalink] New post 18 Dec 2012, 00:33
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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.
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Re: What is the solution set for |3x-2|<=|2x-5| [#permalink] New post 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
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Re: What is the solution set for |3x-2|<=|2x-5| [#permalink] New post 08 Oct 2014, 21:51
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Re: What is the solution set for |3x-2|<=|2x-5|   [#permalink] 08 Oct 2014, 21:51
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