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Starting algebra and I have a problem.

  1. May 21, 2004 #1
    Okay, maybe I just totally missed somthing somewhere, but I encountered a problem while learning "Combination of Terms Equations".

    Here is how they work the problem:



    6x - 2x + 6 = x -2x -16
    4x + 6 = -x + 16
    -6 + -6
    -------------------
    4x = -x + 10
    +x = +x
    ---------------
    5x = 10
    5x = 10
    5----5
    ---------------
    x = 2


    Now, can you explain how they did this? What happend to the '2' and where did the negitive 'X' come from, etc?? Show me how to work this please, because they don't. It seems like they're pulling numbers out of thin air. :grumpy:
     
  2. jcsd
  3. May 21, 2004 #2

    matt grime

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    Homework Helper

    no, they're doing algebraic manipulation:

    i have three times a number, say and i add five times the same number to it, what do i have? 8 times the same number: 3x+5x=(3+5)x=8x

    now you say what happened to the 2, well, i can see 3 of them in there, which one do you mean?

    just treat x as a number and manipulate it according to the rules of arithmetic
     
  4. May 21, 2004 #3

    jcsd

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    6x - 2x + 6= x - 2x - 16

    6x - 2x = 4x and x - 2x = -x therefore we can reduce our equation to:

    4x + 6 = -x + 16

    add -6 to both sides (i.e. takeaway 6 from both sides)

    4x = -x + 10

    add x to both sides:

    5x = 10

    divide both sides by 5:

    x = 2
     
  5. May 21, 2004 #4

    Why do we loose the 2 though? When you subtract by x does it always make it negitive?
     
  6. May 21, 2004 #5
    x - 2x can be written like this:

    1x - 2x

    Replace x with "apple:"

    1apple - 2apples

    You're left with -1apple. That's why:

    x - 2x = -x

    You don't really have to think about what x is doing there. Just think about 1 minus 2:

    1 - 2 = -1
     
    Last edited: May 21, 2004
  7. May 21, 2004 #6
    Okay, thanks! Now it makes sense! :biggrin:

    Thanks guys!
     
  8. May 29, 2004 #7
    shouldnt it be -16 on the second line?
     
  9. May 30, 2004 #8
    Either copied the problem wrong or did the entire equation wrong! 1st line and 2nd line don't match!
     
  10. Jun 4, 2004 #9

    thats the first thing i said,lol, i was thinking "hmmm....that could be your problem right there"
     
  11. Jun 4, 2004 #10
    A false change of sign!

    You are exactly right! The first equation certainly will not balance with x=2.
     
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