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Forum URL: http://www.cut-the-knot.org/cgi-bin/dcforum/forumctk.cgi
Forum Name: College math
Topic ID: 46
#0, RE: Manipulating Equations
Posted by Chris Dann (Guest) on Jan-14-01 at 01:27 PM
I am currently studying with the OU-physics which envolves alot of rearranging equations. There seems to be no literature on how to do this apart from 'you must do the same thing to both sides of the equation.' After trying this i still find on complex equations i get lost ! can anybody help with this ? Either a link to a more complete description, or a lesson from your own knowledge.
cgdann@lineone.net

#1, RE: Manipulating Equations
Posted by alexb on Jan-14-01 at 01:40 PM
In response to message #0
LAST EDITED ON Jan-14-01 AT 01:41 PM (EST)

Most likely the rules for manipulating equations will be found in any decent Algebra 1 text.

I suspect that your problem is not so much with the rules themselves, but with the arithmetic or algebraic operations involved. Why? Because the rules themselves are indeed trivial. Moreover, there are just so many of them. Let A, B, C, ... stand for some mathematical expressions that may or may not include variables. Then

1. If A = B
and C = D,
then A+C = B+D, A-C = B-D, A*C = B*D, A/C = B/D.

(The latter only applicable where neither C, nor D is 0.)

2. If A = B
and c is not 0,
then cA = cB and c + A = c + B.

(This is a particular case of 1, where C = D = c.)

3. If A = B,
and a > 0,
then aA = aB

#2 and #3 examplify that dictum "Whatever you do to the left side do to the right side as well.

All the best,
Alexander Bogomolny