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MathGroup Archive 1999

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

  • To: mathgroup at
  • Subject: [mg19664] Re: Manipulation of equations and inequalities in "high-school style"
  • From: "William M. MacDonald" <wm2 at>
  • Date: Wed, 8 Sep 1999 02:24:13 -0400
  • Organization: University of Maryland
  • References: <7q9hdf$>
  • Sender: owner-wri-mathgroup at

In article <7q9hdf$o62 at> , silvano at (Silvano 
D'Orazio) wrote:

> 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
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Note that a List can be handled just the way that you would handle an
equation.  This means that you can do the following to take the log of both
or to multiply by 2
     ( 2 (eq/.Equal->List))/.List->Equation
You can write a procedure to allow you to manipulate an equation, add two
different equations to cancel terms, etc.

    The other solution is to write an equation that is to be manipulated as
a two-element List.  Then you can operate on it just the way that scientists
and engineers do, i.e.

    eq={2 x + a, x-b}
2 eq
    {4 x + 2 a, 2 x - 2 b}
    {ArcSin[2 x + a], ArcSin[x-b]}


I have repeatedly suggested to Wolfram technical staff, and to Stephen
Wolfram, that Equal be given the same properties for a single equation as
List, that Listable symbols operate on


just as they do on


William M. MacDonald
Professor of Physics
University of Maryland

Internet: wm2 at

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