Results 1 to 8 of 8

Math Help - Inequalities

  1. #1
    Junior Member
    Joined
    Jan 2011
    Posts
    49

    Inequalities

    If 0<a ≤b ≤ c then b<a+c and a<b+c follow automatically.

    I do not understand why b<a+c and a<b+c will follow automatically. Can you please explain? Thank you in advance!
    Last edited by Ackbeet; May 28th 2011 at 11:03 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by Anna55 View Post
    If 0<a ≤b ≤ c then b<a+c and a<b+c follow automatically. I do not understand why b<a+c and a<b+c will follow automatically. Can you please explain? Thank you in advance!
    Given that 0<a\le b do you see why b\le b+a~?
    Last edited by Ackbeet; May 28th 2011 at 11:04 AM. Reason: Improved formatting in quote.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2011
    Posts
    49
    Yes I understand your example. If I plug in values into the original inequalities, I see that it is correct, however I would not be able to write that the two inequalities would follow automatically since I do not understand that fully.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by Anna55 View Post
    Yes I understand your example. If I plug in values into the original inequalities, I see that it is correct, however I would not be able to write that the two inequalities would follow automatically since I do not understand that fully.
    Would you agree that if 0<a\text{ then }x<a+x\text{ for any real number }x~?

    If you do then let x=b~\&~x=c.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2011
    Posts
    49
    I almost understand your example. This is my attempt to use your method on the original problem.
    0<a≤ b≤c
    I replace a and b with x.
    0< a≤ x≤ x
    a-x ≤ x-x
    0<a-x<0<x
    <a-x≤x

    Where is my error or how can you continue with solving the inequality?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,957
    Thanks
    1631
    The original problem says nothing about subtraction. Why are you subtracting x?
    Also, you cannot use "x" to represent both a and b which may be different numbers.

    Do you understand that adding a positive number to any expression makes it larger? That is, if a> 0, b< b+ a for any b.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Anna55 View Post
    If 0<a ≤b ≤ c then b<a+c and a<b+c follow automatically.
    I do not understand why b<a+c and a<b+c will follow automatically. Can you please explain? Thank you in advance!
    a>0

    b\le\ c\Rightarrow\ b<\;\; any\; value\; greater\; than\; c

    c+a>c

    Try the 2nd one.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Quote Originally Posted by Anna55 View Post
    If 0<a ≤b ≤ c then b<a+c and a<b+c follow automatically.

    I do not understand why b<a+c and a<b+c will follow automatically. Can you please explain? Thank you in advance!

    Perhaps you'll understand these inequalities better if you put a, b and c on x-axis.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. inequalities
    Posted in the Algebra Forum
    Replies: 7
    Last Post: August 20th 2011, 04:56 AM
  2. inequalities
    Posted in the Algebra Forum
    Replies: 0
    Last Post: March 20th 2011, 02:42 AM
  3. Inequalities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 1st 2009, 04:35 AM
  4. Inequalities
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 15th 2009, 11:26 AM
  5. inequalities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 14th 2008, 09:57 PM

Search Tags


/mathhelpforum @mathhelpforum