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  =--=--=

```

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