Results 1 to 9 of 9

Math Help - Distributive Property and Absolute Value?

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    7

    Question Distributive Property and Absolute Value?

    OK...so something doesn't seem right when I distribute a positive number versus a negative number into an absolute value. Can someone please explain this to me.

    For example...it was a couple of inequality problems that caught my attention on this:

    -2 abs(3x - 4) < 16

    versus

    3 abs(2x + 5) > 9

    I don't think you can distribute a negative into absolute value...or can you? Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2009
    Posts
    13
    You can distribute only nonnegative numbers into absolute values. With -2 |3x - 4|, you can distribute the 2 but the negative sign must stay outside.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    7

    ok...

    So what do you do with the negative outside of the parentheses if you leave it there? Can someone show me an example or a place on the web where it explains this. It would be nice if I could at least see the first example I posted worked out...

    Anyone???
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Are you sure (-2) |3x-4| < 16 is the right inequality?!

    Since the absolute value is always non-negative, multiplying it by a negative value will always yield a non-positive result and thus obviously lesser than 16 (a positive value)!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2008
    Posts
    7

    yes...

    That is the problem that was given to me in an exercise to work out...is it impossible to do? I just don't get it...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    It's possible! There's just no use playing with it as it can easily be seen that it is correct for any x
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2008
    Posts
    7

    bad example...

    OK...so I guess that was a bad example to use for me to understand exactly how to do this. Can you post a few examples or rules that I can follow and learn? Anyone?!?!

    -2 abs(x + 5)

    -5 abs (-x - 6)

    -7 abs (x - 2)

    Do the rules change if the above examples were equations or inequalities?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Quote Originally Posted by sdudley24 View Post
    OK...so I guess that was a bad example to use for me to understand exactly how to do this. Can you post a few examples or rules that I can follow and learn? Anyone?!?!

    -2 abs(x + 5)

    -5 abs (-x - 6)

    -7 abs (x - 2)

    Do the rules change if the above examples were equations or inequalities?
    No, they don't. Consider this:

    Is -2 * |-5| equal to |(-2)(-5)|? Of course not:

    -2 * |-5| = -10 \neq 10 = |(-2)(-5)|

    If we want to solve, for example, -2|x+5| = -12 then we will do it like this:

    Divide both sides by -2:

     |x+5| = 6 \Rightarrow x+5 = 6 or x+5 = -6 \Rightarrow x_1 = 1; x_2 = -11
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    May 2008
    Posts
    7

    better...

    OK...that helped me out...and if anyone else wants to add to this whole concept, I would greatly appreciate it.

    Thanks so much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Distributive Property
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 10th 2011, 05:19 PM
  2. Help with distributive property
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 11th 2011, 08:36 PM
  3. Why do we want the distributive property?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 18th 2011, 03:14 PM
  4. Please HELP! Distributive property
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 3rd 2010, 10:29 PM
  5. Distributive property
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 16th 2008, 06:40 PM

Search Tags


/mathhelpforum @mathhelpforum