harshavardhanc wrote: rocky,

we should not subtract the inequalities. Addition is okay if the inequalities have the same sign.


see this :

1) 3 > 0
2) 7 > 0

will (1) - (2) be greater than 0? no.

we can tell that (2) - (1) > 0 BECAUSE we know that 7>3.

But in the inequality, like one above, we are not sure which one is greater because of the variables. Hence, subtraction should not be done.

HTH.

You can add or subtract a variable expression on both sides .

Ex :

y + x < 5
-y - y
----------------------
x < 5 - y


another example .

x - ab < 9
+ ab + ab

---------------------
x < 9 + ab

neoreaves wrote:hmmm ...ok now on second thought....we can not subtract inequalities as suggested by harsha ...though good thing we are discussing this right now to keep our concepts in check

neoreaves wrote:If x and y are integers and x>0, is y>0?
1. 7x-2y>0
2. -y<x

harshavardhanc wrote:

rockeyb wrote:

Ashish8 wrote:

rockeyb wrote: Multiply both sides by 7 -------> 7x + 7y > 0

Subtract 1 and 2

7x - 2y > 0
-7x - 7y > 0
-----------------
0 - 9y > 0


- 9y > 0 this is only possible when y < 0 .

Rocky, is this a valid operation? I don't think you can subtract inequlities like that cause at the same time you're multiplying the whole inequlity by -1. Which would make the equation:

-7x -7y < 0

This flips the sign and then a simple addition of the two equations is not possible.

Bro ,

I know we can add or subtract inequalities and equations consisting inequalities . Even we can solve simultaneous equations using inequalities .

The only operation which you need to look out for are multiplication and division by negative number as that will flip the inequality sign .

But I can see your point here . But the thing is we are not trying to multiply both sides of the equation , instead we are subtracting one equation from another .

If we multiply both sides by -1 then the sign would flip . In case of adding or subtracting inequalities we just need to line up the inequalities and perform addition and subtraction as we would do with equality sign.

rocky,

we should not subtract the inequalities. Addition is okay if the inequalities have the same sign.


see this :

1) 3 > 0
2) 7 > 0

will (1) - (2) be greater than 0? no.

we can tell that (2) - (1) > 0 BECAUSE we know that 7>3.

But in the inequality, like one above, we are not sure which one is greater because of the variables. Hence, subtraction should not be done.

HTH.