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.

 

[CellCoree]

for your question. Multiplying two inequalities is not a valid mathematical operation. Inequalities can only be added or subtracted if they have the same direction (both less than or both greater than). In this case, the two inequalities do not have the same direction, so they cannot be multiplied. It is important to follow the rules of mathematics to ensure accurate and valid results.