SUBTRACTING INEQUALITIES

[vishal205]

I have a question regarding the subtraction of two inequalities.
eg:

ineq 1- a+b>0
ineq 2- a-b>0

from 1 we get a>-b...............(3)
from 2 we get a>b................(4)

if v subtract (4) from (3)
do we get 0>-2b ?

or do the signs change..making the above result impossible

[Nikki Veggie]

Certainly not a math whiz, but I believe your result is possible
you get the same answer by subtracting the two inequalities from each other to solve:

ineq 1 a+b >0
ineq 2 a-b >0

when you subtract the two inequalities from each other to solve you get...

a+b >0
-a+b > 0
=
2b>0

now this is equal to your answer because with inequalities when you divide and muliply by a negative the sign flip so...

your answer: 0>-2b

if you multiply both sides by -1 you get
0< 2b or 2b>0
(because you have to flip the sign.)

That is equal to the above, so I believe this possible. By solving it both ways you get the same answer.

Subtracting you don't switch the sign for inequalities. For mulitiplication and division you do.

[vishal205]

Hmm i get your point but isnt subtracting like adding after multiplying the other inequality by -1.

[tim]

exactly, but if you multiply an inequality by -1 the direction flips. this is why you should NEVER subtract inequalities..