inequality

[coolfire_khan]

Hi,

I just wanted to make sure that can we cross multiply inequalities?

for eg if i have this question

1/p> r/(r^2+2)

can we rephrase it like this

r^2+2>pr

OR

if we have
(m+x)/(n+X)> m/n
so can we cross multiply this equality and reduce it to
n>m??

Please clearify..

[cfaking]

Yes, you are right
provided other conditions such as " x Not equal to Zero(in 2nd case) etc"..are met

pls Note

> changes to < only when you change the Sign on both sides

like
say if (-)x/y > (-) p/q
then the following is true
=>x/y < p/q

[ankit.ankitagrawal]

Yes, you are right
provided other conditions such as " x Not equal to Zero(in 2nd case) etc"..are met

pls Note

> changes to < only when you change the Sign on both sides

like
say if (-)x/y > (-) p/q
then the following is true
=>x/y < p/q

I would like to add my 2 cents on it.. We should not ever cross multiply inequalities is we are not sure about the sign of variables involved.. The reason behind this is if we multiply anything negative to both the sides the inequality is reversed.

Example:

2 < 3

Multilpying by 2 both sides we get

4 < 6 which is true

But, multiplying by -2 both sides we get

-4 < -6 which is false, so we should reverse the inequality as well when multiplying with negative. therefore after reversing the inequality we get -4 > -6 which is true..

HTH!!!

[coolfire_khan]

Yes, you are right
provided other conditions such as " x Not equal to Zero(in 2nd case) etc"..are met

pls Note

> changes to < only when you change the Sign on both sides

like
say if (-)x/y > (-) p/q
then the following is true
=>x/y < p/q

I would like to add my 2 cents on it.. We should not ever cross multiply inequalities is we are not sure about the sign of variables involved.. The reason behind this is if we multiply anything negative to both the sides the inequality is reversed.

Example:

2 < 3

Multilpying by 2 both sides we get

4 < 6 which is true

But, multiplying by -2 both sides we get

-4 < -6 which is false, so we should reverse the inequality as well when multiplying with negative. therefore after reversing the inequality we get -4 > -6 which is true..

HTH!!!

Thanks both of you...:)

[cfaking]

agreed
thats why we shd not cross multiply in the case

1/p> r/(r^2+2)

becoz p could be +ve or -ve
we never know

[Ben Ku]

There are a lot of good replies on this one. Just remember that "cross multiplication" is a name we give for multiplying both sides by the denominator of a proportion (two fractions that are equal to each other). In an inequality, however, we cannot multiply variables if we do not know their sign. This is a common trap for test-takers.