Re: Manipulation of equations and inequalities in "high-school style"

*To*: mathgroup at smc.vnet.net*Subject*: [mg19629] Re: Manipulation of equations and inequalities in "high-school style"*From*: phbrf at t-online.de (Peter Breitfeld)*Date*: Mon, 6 Sep 1999 04:20:43 -0400*Organization*: das ist ein breites Feld ...*References*: <7q9hdf$o62@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Silvano D'Orazio <silvano at iprolink.ch> schrieb: > Does anybody know a Mathematica (3 or 4) package which allows > manipulaton of equations and inequalities like high-school students > are supposed to do? > > For example > > 2x+a = x-b subtract a > 2x = x-b-a divide by 2, subtract x > x = -b-a > > or > > (2^x-1)^(1/2) = 5b log both sides > (1/2)(x-1)log2 = log5 + logb multiply by 2, divide by log2 > > > 2(log5 + logb) add 1 > x-1 = -------------- > log2 > > and so on. > > I think I saw such a notebook or package some years ago, but I am not > able to find it any more. > I think I am not the only teacher who would find this very useful. > Thanks for all hints. > > Silvano D'Orazio > I use the following function to do this: GleichungsVerkn[verkn_]:= Module[{ver}, ver=verkn /.Equal->List/.List->Equal; ver[[1]]=Simplify[ver[[1]]]; ver[[2]]=Simplify[ver[[2]]]; Return[ver] ] your second example is now done like this: In[1]:=eq = (2^(x - 1))^(1/2) == 5b Out[1]= ... In[2]:=eq=GleichungsVerkn[Log[eq]]//PowerExpand Out[2]=1/2(-1 + x) Log[2] == Log[5] + Log[b] In[3]:=GleichungsVerkn[2/Log[2]eq+1] Out[3]=x == 1 + (2 Log[5b])/Log[2] With this function you can compose equations too, so e.g. GleichungsVerkn[(a==b)+(c==d)] returns a+c==b+d Peter -- =--=--=--=--=--=--=--=--=--=--=--=--= http://home.t-online.de/home/phbrf Peter Breitfeld, Saulgau, Germany PGP public key: 08548045 =--=--=