       • 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

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