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

• To: mathgroup at smc.vnet.net
• Subject: [mg19598] Re: Manipulation of equations and inequalities in "high-school style"
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 4 Sep 1999 01:34:30 -0400
• Organization: University of Western Australia
• References: <7q9hdf\$o62@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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.

Here is a short Notebook which illustrates one way of doing this.

Notebook[{
Cell[TextData[{
"If you modify ",
Cell[BoxData[
FormBox[
StyleBox["Equal",
" (following Maeder) so that ",
Cell[BoxData[
FormBox[
StyleBox["Listable",
" operations are automatically applied to both sides of any equality,"
}], "Text",
CellTags->{"Equal", "Listable"}],

Cell[BoxData[

Cell[BoxData[
MemberQ(Attributes(f), Listable)\)], "Input"],

Cell[BoxData[
lhs : f_Symbol?
listableQ[___, \ _Equal, \ ___]\  := \n\ \ \ \ \ \ \ \ Thread[\
Unevaluated[lhs], \ Equal\ ]\)], "Input"],

Cell[BoxData[

Cell[TextData[{
"you can directly manipulate equations, ",
StyleBox["e.g.",
FontSlant->"Italic"],
","
}], "Text"],

Cell[BoxData[
\(TraditionalForm\`\(a + 2\ x == x - b;\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[

Cell[BoxData[
\(TraditionalForm\`2\ x == \(-a\) - b + x\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[

Cell[BoxData[
\(TraditionalForm\`x == \(-a\) - b\)], "Output"]
}, Open  ]],

Cell["or", "Text"],

Cell[BoxData[
\(TraditionalForm\`\(\ at 2\^\(x - 1\) == 5\ b;\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
FormBox[
RowBox[{"Simplify", "[",
RowBox[{\(log(%)\), ",",
RowBox[{"x", "\[Element]",
TagBox["\[DoubleStruckCapitalR]",

Cell[BoxData[
\(TraditionalForm\`1\/2\ \((x - 1)\)\ \(log(2)\) ==
log(5\ b)\)], "Output"]
}, Open  ]],

Cell[TextData[{
"Note that ",
Cell[BoxData[
FormBox[
RowBox[{"x", "\[Element]",
TagBox["\[DoubleStruckCapitalR]",
" is required here. Then we can proceed:"
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[

Cell[BoxData[
2\ \(log(5\ b)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[

Cell[BoxData[
1 == \(2\ \(log(5\ b)\)\)\/\(log(2)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[

Cell[BoxData[
\(TraditionalForm\`x == \(2\ \(log(5\ b)\)\)\/\(log(2)\) +
1\)], "Output"]
}, Open  ]]
}
]

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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