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Multiplying the two inequalities 
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#1
Mar1214, 03:26 PM

P: 71

Lets suppose we have two inequalities,
First inequality is xy≤ab≤x+y Second inequality is tg≤cd≤t+g How can I multiply these inequalities Thanks 


#2
Mar1214, 03:55 PM

Sci Advisor
P: 6,062

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.



#3
Mar1314, 12:08 PM

P: 71

Thanks



#4
Mar1614, 07:36 AM

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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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