Multiplying the two inequalities

[Quarlep]

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

Thanks

 

[mathman]

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]

Thanks

 

[arildno]

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.