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omomo
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aboslute value inequalities 23 Oct 2005, 10:07
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|3x-2|<=|2x-5|

Hi,
Can someone let me know if there's another approach to solve this problem besides squaring both sides to remove the absolute value inequalities first?

Thanks.



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aboslute value inequalities 23 Oct 2005, 10:38
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If there is nothing mentioned about x, for x=0, this is false. For -ve integer values of x, it is true and for positive values it is true.
Can you please post the whole question?
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aboslute value inequalities 23 Oct 2005, 11:02
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gsr
If there is nothing mentioned about x, for x=0, this is false. For -ve integer values of x, it is true and for positive values it is true.
Can you please post the whole question?
Show more

This is the original question:
Find the solution set for the following inequalities |3x-2|<=|2x-5|

The first step of the explanatory answer for this question from 4gmat ebook is squaring both sides to get rid of the absolute value sign.
(3x-2)^2<=(2x-5)^2

However, I read once that
Quote:
"Another way to eliminate an absolute value is to square both sides of the equation. Taking the absolute value makes things non-negative, and squaring makes things non-negative. So, if you square something, you no longer need to take its absolute value. However, be careful when squaring both sides of an equation as this can lead to extraneous solutions."
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from https://www.richland.edu/james/lecture/m116/prerequisites.html

Thus, I would like to know if there's an approach other than squaring both sides.

Let me know if you want to see the OE.
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aboslute value inequalities 24 Oct 2005, 10:41
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Is the answer the following?

x <= 7/5
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aboslute value inequalities 24 Oct 2005, 10:57
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For the record, I came up with x <= 7/5 by using the squaring method. Frankly, I think it's easier than trying to pick numbers to come up with an answer. For this problem, squaring is the much easier method.

|3x-2| <= |2x-5|
(3x-2)^2 <= (2X-5)^2
9x^2 - 12x + 4 <= 4x^2 - 20x + 25
5x^2 + 8x -21 <= 0
(5x-7)(x+3) <= 0
x <= -3 or 5x <= 7
x <= -3 or x <= 7/5

Because we know that x is <= either -3 or 7/5, take the larger number, 7/5.
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aboslute value inequalities 08 Nov 2005, 18:36
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If you dont want to square both sides, then here is the other way, which is usually shorter, however, I found that it is lengthier/error prone for me for this question:

for x x = 3

for x 5/2
x >= 3/5

for x > 2/3 and x 2/3 2/3 and x > 5/2 => x > 5/2
x <= -3

The only solution that is valid for range is x < 7/5 for 2/3 < x < 5/2



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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