Algebra 1 Variables
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More X's
Variables

 

 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

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