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 Subject: RE: Is 'variable' confusing to students? Author: The Math Guy Date: May 8 2009
In 11 = 3x + 5, the x can and does vary.  When X = 2, the statement is true.
And when it is not, then the statement is false.  But it can take on many
values.  We don't often enough talk about the truth/falseness of the statement
and only at the case when it is true.

On May  8 2009, Susan wrote:
> I'm trying to establish the differences among the following three
> things:

3x + 5

11 = 3x + 5

y = 3x + 5

The first is an
> algebraic expression containing the "variable" x.  In this case, the
> variable x can take on any value.  It “varies”.

The second is an
> equation of one variable.  We call x a variable but truly it doesn't
> vary.  It is just an "unknown".  We can solve for x and determine it
> must equal 2.

In the final case, we have two variables and they
> do 'vary' depending on each other’s values.

Should we call the x
> in the second case an “unknown” and not a variable?   I’ve seen
> books say, “solve for the unknown”.

I think we confuse students
> by calling x “variables” in all of these cases when in case 2, the x
> does not vary at all.