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Prove the inequality?

  1. Apr 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove: If a>b and c>d, then a+c>b+d
    Hint: (a-b)+(c-d)=(a+c)-(b+d)>0

    2. Relevant equations

    3. The attempt at a solution

    How to use the hint to prove the inequality?
    My method, not sure it's right.
    Given c>d, c-d>0
    Given a>b => a+(c-d)>b
    Thus a+c>b+d
  2. jcsd
  3. Apr 25, 2012 #2


    Staff: Mentor

    Re: Inequalities

    Why not continue with the same line of thinking as above?

    a > b implies what about a - b?
  4. Apr 25, 2012 #3
    Re: Inequalities

    ok i see it now

    Given a>b =>a-b>0
    Given c>d =>c-d>0

    thus a+c>b+d

    thank you
  5. Apr 25, 2012 #4


    Staff: Mentor

    Re: Inequalities

    You're welcome!
  6. Apr 26, 2012 #5


    User Avatar
    Science Advisor

    Re: Inequalities

    Another way to do this, and, in my opinion, simpler, is this:
    Since a> b, a+ c> b+ c.
    Since c> d, b+ c> b+ d.
    Since ">" is transitive a+ c> b+ d.
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