Re: New user: Abs[] problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg50107] Re: [mg50079] New user: Abs[] problem*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sun, 15 Aug 2004 03:14:38 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200408140550.BAA15327@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

Yes, sometimes Mathematica cannot find (all) solutions. But in this case, BELIEVE! Mathematica DID solve it: there are no solutions! You can see this, e.g., by graphing your piecewise-linear function: Plot[x + 1 + Abs[2x - 4] + Abs[5 - x], {x, -10, 10}]; Plot[x + 1 + Abs[2x - 4] + Abs[5 - x], {x, 0, 5}]; (The second Plot is just to convince you that the minimum really is strictly positive.) Or, you can consider the 4 cases: case1 = x >= 2 && 5 >= x; case2 = x >= 2 && 5 < x; case3 = x < 2 && 5 >= x; case4 = x < 2 && 5 < x; The first case gives the closed interval from 2 to 5; the second and third simplify... Reduce[case2, x] x>5 Reduce[case3, x] x<2 ... and the fourth case gives the empty set: Reduce[case4, x] False (You could have done that much without Mahematica, of course.) Now look at your function of x on each of these intervals: expr = x + 1 + Abs[2x - 4] + Abs[5 - x]; lin1 = Simplify[expr, case1] 2(1+x) lin2 = Simplify[expr, case2] 4 (-2 + x) lin3 = Simplify[expr, case3] -2 (-5 + x) Now try to solve the resulting linear equation in each case: Solve[lin1 == 0, x] {{x->-1}} Solve[lin2 == 0, x] {{x->2}} Solve[lin3 == 0, x] {{x->5}} In each case, the line meets the x-axis at a point outside the interval on which the corresponding line segment over the interval in question is the domain of the piece. QED Edson.Brusque at smc.vnet.net wrote: > Hello, > > I'm starting Electrical Engineering and using Mathematica for > helping me in Calculus e Algebra studies. > > I'm trying to solve this equation on Mathematica: > x + 1 - |2x - 4| + |5 - x| = 0 > > on the Math* notebook I'm typing: > Solve[x + 1 - Abs[2x - 4] + Abs[5 - x] == 0,x] > > but only got an empty output: {{}} > > Someone please can help me get Math* to solve this? -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**Follow-Ups**:**Re: Re: New user: Abs[] problem***From:*DrBob <drbob@bigfoot.com>

**Re: Re: New user: Abs[] problem***From:*Murray Eisenberg <murray@math.umass.edu>

**References**:**New user: Abs[] problem***From:*Edson.Brusque@smc.vnet.net