



When
we started working with X's we had problems like this ... 





3X  5 = 0






Then
we solved for X. 





Now,
we are going to look at ... 





3X  5 = ?






Instead
of a zero, we've got a question mark on the right side. 


Here
the game is, feed in a number for X 


and
see what the ? turns out to be. 


If
X = 2, then ... 


3(2)
 5 = ? 



6
 5 = ? 



1
= ? 






So
when X = 2, the question mark equals 1. 





If
X = 7, then ... 


3(7)
 5 = ? 



21
 5 = ? 



26
= ? 






We
can chose anything that we want for X 


and
then figure out what the question mark is. 





Before
when we had a question mark in the problems, 


math
people said: 


"Yuk, we
can't have a question mark in an equation."



"that
looks terrible!" 


"Use
an "X" instead" 





Guess
what, 


math
types still don't like question marks in equations. 





X
is already busy, so they got the next best thing. 


So
what's next to X ? 





Y






So
instead of writing ... 


3X  5 = ?






We
write ... 


3X  5 = Y






But
it means the same thing! 





So
now when we choose 2 as the value of X (X = 2), 


we
get ... 


3(2)
 5 = Y 



6
 5 = Y 



1
= Y 






When
we choose 7 for X (X = 7) 


we
get ... 


3(7)
 5 = Y 



21
 5 = Y 



26
= Y 






OK,
I know it's not a big change, 


but
sometimes math people are easily amused. 





We
could be here until the end of time 


choosing
values for X and seeing what we get for Y, 


but
life's too short. 


We
need a new way to look at this kind of equation. 





Maybe
we could just have something that we could look at, 


and
know that if X was this then Y was that 


without
having to do the math for each and every number. 


We
need to be able to see the BIG PICTURE. 





POP
QUIZ 


Guess
what's on the next page? 





copyright 2005 Bruce Kirkpatrick 
