Re: Help with this!!!! please

*To*: mathgroup at smc.vnet.net*Subject*: [mg4169] Re: Help with this!!!! please*From*: Count Dracula <lk3a at kelvin.seas.virginia.edu>*Date*: Sat, 8 Jun 1996 13:26:11 -0400*Organization*: University of Virginia*Sender*: owner-wri-mathgroup at wolfram.com

In Message-ID: <4p35kc$n9o at dragonfly.wolfram.com> "Erick Houli Katz" <ehk at netpoint.net> writes: > How can I solve this exercise? > |1-2X|+|3X+1|=2 Let f(X) = | 1 - 2 X | + | 3 X + 1 |. (1) First suppose X >= 1/2, i. e., 1 - 2 X <= 0. Then f(X) = -(1 - 2 X) + ( 3 X + 1 ) = 5 X >= 5/2 > 2 and there is no X >= 1/2 for which f(X) = 2. (2) Next suppose X < 1/2. If 3 X + 1 >= 0, i. e., X >= -1/3, then f(X) = 1 - 2 X + 3 X + 1 = 2 + X and f(X) = 2 for X = 0. If, on the other hand, X < -1/3, then f(X) = 1 - 2 X - (3 X + 1) = - 5 X and f(X) = 2 if X = -2/5. So the solutions are X = 0 and X = -2/5. -- ___________________________________________________________________________________ Levent Kitis lk3a at cars.mech.virginia.edu lk3a at kelvin.seas.virginia.edu University of Virginia Department of Mechanical, Aerospace, and Nuclear Engineering ==== [MESSAGE SEPARATOR] ====