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#2 (permalink) | |
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Eager!
Join Date: Oct 2004
Location: Bucharest
Posts: 65
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Quote:
1) x is between (3;4) 2) x is between (-14 ; -5) U [-1; 8) 3) x < - 2.5 |
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#6 (permalink) | |
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Within my grasp!
![]() ![]() Join Date: Mar 2005
Posts: 386
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Quote:
x<=-8 -x-8<-x+3 -8<3 x<=-8 -8<x<3 x+8<-x+3 -8<x<-2.5 x>3 x+8<x-3 8<-3 ![]() overall x<-2.5
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#7 (permalink) |
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Grrr...
![]() ![]() ![]() ![]() Join Date: Apr 2005
Posts: 1,268
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Solutions:
1) |x^2 - 7x + 12| > x^2 - 7x + 12 If |y| > y, clearly y<0 Similarly, x^2 - 7x + 12 < 0 => (x-4)(x-3) < 0 Therefore, 3 < x < 4 ------------------------------------------------------------------------- 2) 2 <= |x+3| < 11 Textbook approach: Break into 2 inequations i) |x+3| < 11 implies -11 < (x+3) < 11 implies -14 < x < 8 ii) |x+3| >= 2 implies x >= -1 OR x <= -5 Merging the 2 solution sets gives, -14 < x <= -5 OR -1 <= x < 8 Number line method: http://mathforum.org/library/drmath/view/53126.html I find that sketching a quick graph, helps me see the answer immediately ------------------------------------------------------------------------- 3) |x+8| < |x-3| Clearly, x<0 We have 2 inequations: i) -(x+8) < -(x-3) --------> where (x+8) <= 0 implies -8 < 3 ---> Insightful! ii) (x+8) < -(x-3) ---------> where (x+8) > 0 implies x < -5/2 Therefore, x < -5/2 Last edited by arjmen : 2005 July 22nd at 10:10 AM. Reason: formatting |
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#9 (permalink) |
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TestMagic Guru-in-Training
![]() ![]() ![]() Join Date: May 2005
Location: Jersey City
Posts: 921
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|x+8| < |x+3|
From the above, there can be 4 equations possible. -(x+8)=-(x+3) ==> (x+8)=(x+3) -(x+8)=(x+3) ==> (x+8)=-(x+3) (x+8)=-(x+3) (x+8)=(x+3) From the above you can see that there are actually 2 equations only. How you want to put - and + on both side of equations depends from each person I think ![]() |
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