1. |(2/x) - 4| < 3

This is really two inequalities:

-3 < (2/x) - 4 < 3

So add 4 to all "three" sides:

-3 + 4 < (2/x) - 4 + 4 < 3 + 4

1 < 2/x < 7

So 1 < 2/x and 2/x < 7

The first gives:

0 < 2/x -1

0 < (2-x)/x

which is positive for x < 2.

The second gives:

2/x < 7

2/x - 7 < 0

(2-7x)/x < 0

which is negative for x > 2/7.

So 2/7 < x < 2.

-Dan