Conditions for which inequalitys is true

[transgalactic]

A:
1-mt<w^2(m+t)

B:
-(1+mt)<(w^2 )t(m-t)


i have 4 cases
for each case they said that needs to be a condition for which this case would be true
1: m>t and mt<1
so they say that i have to demand
w^2>(1-mt)/(m+t) which is inequality A

2: m<t and mt<1
they say that i have to demand
inequalitys A and B

why ??

 

[HallsofIvy]

A:
1-mt<w^2(m+t)

B:
-(1+mt)<(w^2 )t(m-t)


i have 4 cases
for each case they said that needs to be a condition for which this case would be true
1: m>t and mt<1
so they say that i have to demand
w^2>(1-mt)/(m+t) which is inequality A

2: m<t and mt<1
they say that i have to demand
inequalitys A and B

why ??

If m< t, m- t is negative, if m> t, m- t is positive, if mt< 1, 1-mt is positive and w^2 is always positive.

 

[transgalactic]

so why in case two they demand both ??
it seems like the left side is true always
it cannot be negative?

 

[transgalactic]

why in the 1st case we only pick only one innequality
??

 

[transgalactic]

even if i substitute what you say regarding the positive and negative
i get
positive>positive

so??

 

[transgalactic]

wwoowww thanks i understood that stuff
:)