



Now
let's get a little trickier ...






I'm
thinking of a number. 


If you
multiply the number by 3 you get 12. 


What's
the number? 





Translated
into X stuff, this is: 





3
× X = 12






To save
space, we write this as: 





3X
= 12






When you
an X's, and it is multiplied by something (like 3) 


you just
write 3X and not 3 x X. 


It's
like, 


if you
had 3 apples, you'd just write "3 apples", 


not
"3 x apples". 





OK, so
we've got 3X = 12. 


Adding or
subtracting stuff won't help us here. 


We need
another way to get the X by itself. 





Here it
is: 











There is
a 3 that is multiplied times the X. 


So to get
rid of it we divide both sides by 3 ... 











and
simplify ... 











And a 1
in the denominator doesn't change anything 


so we can
get rid of them ... 





X
= 4






Swell,
here's another one ... 





7X = 35






So this
time there is a 7 multiplied times the X 


To get
rid of it we divide both sides by 7 ... 











and then
simplify ... 











This
time, we didn't even bother to write the 1's 


in the
denominators. 





Now an
even trickier one ... 











This one
might need some explaining ... 





What we
have been doing up to now, 


is
turning the number next to the X into 1. 


That is,
we multiply by whatever we need to, 


to turn
the number next to the X into a 1. 





Here, the
number next to the X is ^{1}/3. 


What do
you multiply ^{1}/3
by to get 1? 


You need
to multiply it by 3. 





So ... 











We might
also have a problem with X in it more than once. 





We might
have ... 





3X
+ 2  X = 12






So the
first thing that you need to do 


is to
combine the 3X and the X. 


3X  X =
2X 


(it's
like 3 apples minus 1 apple equals 2 apples) 





So now
we've got: 





2X
+ 2 = 12






Now we
need some subtraction ... 











and some
division ... 











One last
note: 


Any time
we have a number or an X or things 


multiplied
together, it is called a term. 


So these
are all terms: 





3X
4
5
12X






These are
NOT: 





3X
+
5
3  X






Those
last two were two terms each. 


Terms are
usually separated from each other 


by a plus
or minus sign. 





copyright 2005 Bruce Kirkpatrick 
