Simple Question

Discussion in 'Math' started by Tekker, Oct 16, 2005.

  1. Tekker

    Thread Starter Active Member

    Apr 22, 2005
    33
    0
    I'm currently taking math 111 right now (algebra) so this should be an easy question to answer for you guys. :D I haven't had math in over a couple years, and I definitely wasn't very into math at the time so I've long forgotten all this "review" stuff. LOL

    Basically, what I want to know is for this equation:

    Code ( (Unknown Language)):
    1.  
    2.   1     1     3
    3. --- + --- = ----
    4.   t     6     2t
    5.  
    Why can't I just invert both sides of the equation and solve for t? When I do that I get:

    Code ( (Unknown Language)):
    1.  
    2.                 2t
    3. 3 * (t + 6) = ---- * 3
    4.                 3
    5.  
    6. 3t + 18 = 2t
    7.  
    8. t = -18..... ???? (the answer is supposed to be 3)
    I know what the proper procedure is, I just want to know why this doesn't work, since it apparently doesn't. I know that you can do anything to one side of the equation as long as you do it to the other side as well.... So is there some step or rule that I'm missing here, or am I messing something up when solving for t? I need to know why this doesn't work, so I know when not to use this method. ;)

    Thanks.
    -tkr
     
  2. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Hi tekker,

    The quick answer is :

    Code ( (Unknown Language)):
    1.  
    2. To invert the left side of your equation requires that you invert the left side expression as a whole.
    3.  
    4. Since:
    5.  
    6.      1
    7. ----------  does not equal  (t + 6)
    8.   1     1      
    9. --- + ---  
    10.   t     6      
    11.  
    12. Then the techinique you attempted to employ did not yield the correct answer.
    13.  
    Code ( (Unknown Language)):
    1.  
    2. Instead :
    3.  
    4.      1               6t
    5. ----------  =  ----------
    6.   1     1          (t + 6)
    7. --- + ---  
    8.   t     6      
    9.  
    10.  
    Inverting the individual terms in the left side expression is not the same as inverting the expression as a whole.

    Math can be a bit tricky but the real key is to solve many example problems so that the rules govening the algebraic manipulation of expressions becomes clear.

    At least you were curious enough to try something different to arrive at a solution. That shows you are keen to explore new ways to do things. You should do fine in your Math course with that approach.

    Good Luck,
    hgmjr
     
  3. Tekker

    Thread Starter Active Member

    Apr 22, 2005
    33
    0
    I did invert the whole expression (on the right side it used to be 3/2t, then I inverted to be 2t/3 with the rest of the equation on the left side)..... That's why I don't understand why it doesn't come out the same.

    This math stuff is tricksy. :D

    -tkr
     
  4. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Hi tekker,

    You did correctly invert the expression to the right of the equal sign.

    By the term "expression as a whole", I was referring to the expression to the left of the equal sign. I can see how my statement could have been interpreted as referring to the entire expression.

    I plead guilty to not being clear with my statement.

    Code ( (Unknown Language)):
    1.  
    2.  1    1
    3. ---- + ----
    4.  t    6
    5.  
    6. By adding these two terms you get:
    7.  
    8.  6 + t
    9. --------
    10.   6t
    11.  
    12. In this quotient form you can them invert this expression along with the term on the right side of the expression and you will arrive at the correct answer the variable t.
    13.  
    14.  
    hgmjr
     
  5. Tekker

    Thread Starter Active Member

    Apr 22, 2005
    33
    0
    Ahhhh..... *Light comes on* Now I get it!

    In that form it would probably be easier to just solve it now without inverting, whereas before it “appeared” easier to just invert to get rid of the fractions. But now it makes sense why that wouldn’t work. :)

    Code ( (Unknown Language)):
    1.  
    2.   6 + t     3
    3. ------- = ----
    4.     6t      2t
    5.  
    6.           18t
    7. 6 + t = -----
    8.           2t
    9.  
    10. 6 + t = 9
    11.  
    12. t = 3
    13.  
    Fantastic! The way the book mentioned it was to multiply by the lowest common factor (6t) to cancel out the denominator. But in general, this is the way I think. Just solve the problem, so I had to know why my previous solving method didn’t work.... and now I know. Thanks a lot! B)

    -tkr
     
  6. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Hi tekker,

    Those "light bulb" moments are always exciting. The neat part about math is that it is full of them.

    Good luck with the remainder of your math studies.

    hgmjr
     
  7. Tekker

    Thread Starter Active Member

    Apr 22, 2005
    33
    0
    Yep the light bulb moments are great, but the bulb doesn't seem to last for very long. ;) I'm also taking chemistry 201 at the same time so I've got quite a work load this term. Lots of light bulb moments in chemistry also that's for sure.

    Thanks. It's funny because before I got really interested in electronics, I probably would have just looked the answer up in the book, wrote the answer down and not given it another thought.... Which is exactly what I did with all of my previous math classes. But now I'm actually looking forward to learning as much as I can about this stuff (and even chemistry) because I know it'll be worth it when I can apply it all to electronics. It's amazing how much more enjoyable it is when you can actually apply it to something you enjoy. I see how knowlegable you guys are here on the forum and it just blows my mind! :wacko: That's the level that I want to get to eventually. B)

    -tkr
     
  8. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Hi tekker,

    It has been my personal experience that one always excels in any endeavour for which one has a genuine passion.

    It sounds like your enthusiasm is high toward the courses you are taking. That will fuel your dedication to the task of absorbing as much knowledge as you can.

    One of the most important things you can learn is how to continue to expand your knowledge once you complete your formal studies.

    Continue to ask questions along the way.

    Good Luck,
    hgmjr
     
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