1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Absolute value Quest,

  1. Sep 18, 2011 #1
    Absolute value Quest, urgent

    1. The problem statement, all variables and given/known data
    a) |x-2| + |6-3x| = 12x



    2. Relevant equations



    3. The attempt at a solution

    I have a question about y this negetive becomes a positive.. ::

    Steps ::
    |x-2| + -3|x-2|
    |x-2| +3 |x-2| = 12x > this step if i factored out.. |x-2|+[-3]|x-2| , shouldnt it be -3 +1 =2?? why does it become 4
    4|x-2| = 12/4
    |x-2| = 3x
    If i factor out a -3, then add the "1" on the left side it should be -2 no? in my notes its written this way and is correct in the book, why did that -3 become positive?
     
  2. jcsd
  3. Sep 18, 2011 #2
    Re: Absolute value Quest, urgent

    anyone....?
     
  4. Sep 18, 2011 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Absolute value Quest, urgent

    You can not replace |6-3x| by -3|x-2|. The absolute value is never negative, and you made it never positive. Factor out 3, so your equation becomes |x-2| + 3|2-x| = 12x

    Replace |x-2| by 2-x if x-2<0. At the same time, 2-x>0 so |2-x|=2-x.
    What have you do when x-2 >0?

    ehild
     
  5. Sep 18, 2011 #4
    Re: Absolute value Quest, urgent

    Um... okay.. so you cant take out a negetive..

    Then..

    :: |x-2| + |6-3x| = 12x
    :: |x-2| + 3|2-x| = 12x
    :: 4|x-2| |2-x| = 12x/4
    |x-2| |2-x| = 3x.

    Now your telling me to replace 2-x with x-2? because they both need a value of 2 yes?

    So get rid of 2-x and it becomes |x-2|=3x , is that right??
     
  6. Sep 18, 2011 #5
    Re: Absolute value Quest, urgent

    ??? anyone
     
  7. Sep 18, 2011 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Absolute value Quest, urgent

    I do not understand your questions.

    |x-2|=|2-x|, so the sum is 4|x-2|=12x , so |x-2|=3x.

    You have two possibilities: x<2 and x≥2. What is |x-2| in both cases?

    ehild
     
  8. Sep 18, 2011 #7
    Re: Absolute value Quest, urgent

    The two possibilities is not My question. My question is what is happening algebraically to this question inorder for there to only be one |x+1| BRACKET. What happends do other bracket? do they join to become one?

    :: |x-2| + |6-3x| = 12x
    :: |x-2| + 3|2-x| = 12x
    :: 4|x-2| =12x, |2-x| = 12x/4
    |x-2| |2-x| = 3x???. < Why does one of the absolute brackets go away? how do you know which one?

    Now your telling me to replace 2-x with x-2? because they both need a value of 2 yes?

    So get rid of 2-x and it becomes |x-2|=3x , is that right??

    Let me pose another question.

    b) 7|x+2| = 2|x+2| +15

    does this simplify into..

    5|x+2| = 15

    The two brackets were the same so they added and joined, but the two brackets in the first question arent the same, so why would they join and become one? why did it vanish

    I know all about the cases, thats not what im asking, just tryin to figure out the algebra stuff
     
    Last edited: Sep 18, 2011
  9. Sep 18, 2011 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Absolute value Quest, urgent

    |6- 3x|= |-3(x- 2)|= 3|x- 2|
    (That's what meant when he said "you can't take out a negatve"- but you can take out the
    "3". The "negative became a positive" because you are taking the absolute value: |-3|= 3.

    With that, your equation becomes "4|x- 2|= 12x" so that |x- 2|= 3x.
    Of course |x-2|=|2- x|. There is no difference between them because absolute value "strips away the sign". More accurately, if [itex]x-2\ge 0[/itex], so that |x- 2|= x-2, then [itex]2- x\le 0[/itex] so that |2- x|= -(2- x)= x- 2 also. And, of course, if x- 2< 0 so that |x- 2|= -(x- 2)= 2- x, then 2- x> 0 so that |2- x= 2- x. Either way, |x- 2|= |2- x|.
    More generally, |x|= |-x|.

    Now, to complete the problem, consider cases:
    If [itex]x- 2\ge 0[/itex], |x- 2|= x- 2= 4x. Solve that. Is x> 2?
    If x- 2< 0, |x- 2|= -(x- 2)= 2- x= 4x. Solve that. Is x< 2
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Absolute value Quest,
  1. Absolute value (Replies: 3)

  2. Absolute value (Replies: 4)

  3. Absolute values (Replies: 5)

  4. Absolute value (Replies: 2)

Loading...