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# Find the solution set (values of X) for the following

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Director
Joined: 16 Jun 2004
Posts: 893
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Find the solution set (values of X) for the following [#permalink]  08 Sep 2004, 19:45
Find the solution set (values of X) for the following inequality
|3X - 2| <= |2X - 5|. Note <= is 'less than or equal to'
Director
Joined: 20 Jul 2004
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-3 <= x <= 7/5

I solved each of the 4 possible solutions of |3X - 2| <= |2X - 5|

1. (3X - 2) <= (2X - 5)
2. -(3X - 2) <= (2X - 5)
3. (3X - 2) <= -(2X - 5)
4. -(3X - 2) <= -(2X - 5)

1. and 2. gave a result -3 >= x >= 7/5, which is impossible.
3. and 4. gave a result -3 <= x <= 7/5, which seems to be the solution set.
Director
Joined: 16 Jun 2004
Posts: 893
Followers: 2

Kudos [?]: 19 [0], given: 0

Well Done Hardworker.

In this problem, bioth sides of the inequality have modulus and both sides of the inequality has linear functions. Hence, we can square both sides and remove the modulus sign.

then we have,
(3x-2)^2 <= (2x-5)^2
+> 9x^2-12x+4 <= 4x^2-20x+25
=>(x+3)(5x-7)<=0

which is -3<=x<=7/5
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