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Multiplying the two inequalities

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Quarlep
#1
Mar12-14, 03:26 PM
P: 57
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

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mathman
#2
Mar12-14, 03:55 PM
Sci Advisor
P: 6,039
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.
Quarlep
#3
Mar13-14, 12:08 PM
P: 57
Thanks

arildno
#4
Mar16-14, 07:36 AM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Multiplying the two inequalities

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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