MHB What happens when dividing by a negative in an inequality?

[Yazan975]

View attachment 8424

 

[Greg]

-10 < 2x + 3 < -1
-13 < 2x < -4
-13/2 < x < -2

 

[Wilmer]

-c < ax + b < -d

Easier to work with (after re-arranging):
c > -(ax + b) > d

 

[topsquark]

-c < ax + b < -d

Easier to work with (after re-arranging):
c > -(ax + b) > d

But when you get to the step c + b > -ax > d + b you have to divide by -a anyway and the >s flip again. I think it's good in that you get that extra step (to stress the point of what happens when you divide by a negative) but greg1313's method is slightly more efficient.

-Dan

 

[Wilmer]

But when you get to the step c + b > -ax > d + b you have to divide by -a anyway and the >s flip again. I think it's good in that you get that extra step (to stress the point of what happens when you divide by a negative) but greg1313's method is slightly more efficient.
-Dan

Ya...agree...BUT li'l ole me prefers ? > ? > ? to ? < ? < ?
A bit like reading left to right instead of backwards!
Anyway, not important...