Is it just me or?

[alan2here]

Is it just me or do you sometimes find solving equations simpler when you think of things like this where,

 

a = b + c - 2c

 

becomes (mentally even if you don't write it like this)

 

+a = +b +c -2c

 

so everything is signed and any existing signs become attached to the symbols on there right?

 

I say sometimes as mostly I don't find this necessary however when I can't work out what is going on specifically with an equation with lots of negatives in I find it a useful way of thinking about the equation. Each bit then becomes septate and can be thought about more easily.

 

 

example 1:

b + c - 2c

 

parts:

+b

+c

-2c

 

simplified:

b - c

 

 

example 2:

[math]a^2 - 2c = b + 4(c^2 * c^3 + 8) - 2c[/math]

 

side1:

[math]+a^2[/math]

-2c

 

side2:

+b

[math]+4(c^2 * c^3 + 8)[/math]

-2c

 

or side2:

+b

[math]+(c^2 * c^3 + 8)[/math]

[math]+(c^2 * c^3 + 8)[/math]

[math]+(c^2 * c^3 + 8)[/math]

[math]+(c^2 * c^3 + 8)[/math]

-2c

 

or side2:

+b

[math]+4c^5[/math]

+32

-2c

 

 

Of course this is an impractical way of writing it, especially if you are doing it on paper, better to write it in a line.

 

[math]a^2 - 2c = b + 4(c^2 * c^3 + 8) - 2c[/math]

[math]a^2 - 2c = b + 4c^5 + 32 - 2c[/math]

[math]a^2 = b + 4c^5 + 32[/math]

 

Getting from line 2 to line 3 of the above example for example requires for me the thoughts I demonstrated above but not for all the symbols on the line.

 

I don't really know how others think of equations like this as I have taught myself a few weeks ago, mostly algebra but also some other mathematics. The few people I have talked to ether can't do algebra or have been doing it so long they don't know how they solve it at a sufficiently basic level.

 

4c + 8 - 2c

+4c +8 -2c

+4c -2c +8

4c - 2c + 8

 

It's always tempting and more natural seeming to write

 

[math]b + 4(c^5) + 8[/math]

instead of the more correct

[math]b + 4c^5 + 8[/math]

as this to me looks like it could be confused with

[math]b + (4c)^5 + 8[/math]

which of course it can't.

 

And quadratic equations seemed to take an almost superhuman amount of thought to even only mostly understand and I still can't memorize all the rules and methods of how to solve them. But I suspect that applies to nearly everyone.

 

Sorry if this thread doesn't live up to my other more insightful and brilliant scientific threads. I in part need some people to talk to about this stuff, even if it seems insignificant to you it seems important to me.

 

Feel free to test me with something more challenging, include other ideas such as sequences and the such if you wish. I want to test how much I have actually manged to absorb.

Edited September 16, 2008 by alan2here

[CaptainPanic]

Solving these kinds of equations are just good bookkeeping. If you find it convenient to add extra + and (), then go ahead.

 

It is just not true that [math] b + 4(c^5) + 8 [/math] is less correct than [math]b + 4c^5 + 8[/math]. They are mathematically identical, and therefore equally good. Write whatever you find convenient. If you are getting confused, that is actually a terribly good reason to include the ().

 

I'm also a good example of somebody who adds a lot of extra symbols just to avoid mistakes. I know I am always making a mess... I know the rules, but I make stupid small mistakes. You can spend minutes or even hours solving something, but it only takes 1 second to make a mistake. Good bookkeeping is the key here (and knowing the maths of course).

[alan2here]

Thanks :¬)

[I_Pwn_Crackpots]

Yeah, I always use parenthesis to keep myself organized. For signs, only the negative sign is sufficient, I don't also need a positive sign, though I do switch signs often so that they become easier to keep track of.