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

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Director
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Find the solution set (values of X) for the following [#permalink] New post 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
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 [#permalink] New post 08 Sep 2004, 20:05
-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.
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 [#permalink] New post 09 Sep 2004, 13:03
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
  [#permalink] 09 Sep 2004, 13:03
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Find the solution set (values of X) for the following

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