Do you reverse an inequality when taking reciprocals?

[amd123]

Homework Statement

[PLAIN]http://img641.imageshack.us/img641/2494/mathg.png
I've worked through it and at the 1st step I get:
(1/-e+1)<x<(1/e+1)

How do they have
(1/e+1)<x<(1/-e+1)?

Do you switch the signs of an inequality when you take the inverse of both sides?

 

[Dick]

1<2. 1/1>1/2. Yes, you do reverse the inequalities when you invert.