Multiplying the two inequalities

  1. Lets suppose we have two inequalities,
    First inequality is x-y≤a-b≤x+y
    Second inequality is t-g≤c-d≤t+g How can I multiply these inequalities

  2. jcsd
  3. mathman

    mathman 6,747
    Science Advisor
    Gold Member

    What do you have in mind by multiplying inequalities? In any case if all the terms are positive then term by term multiplication is OK. Otherwise be very careful.
  4. Thanks
  5. arildno

    arildno 11,265
    Science Advisor
    Homework Helper
    Gold Member

    If you do not know whether these expressions can be negative, you can't validly multiply inequalities into new inequalities.

    If you DO know that all the 8 individual numbers are, say, positive, you may first rearrange your inequalities, to for example:
    x+b<=a+y<=x+2y+b and THEN multiply with the similary rearranged second inequality.
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