Guide 3, 4th Ed Q10 p191, if 4/x < 1/3

[chuperman601]

If 4/x < 1/3, what is the possible range of values for x?

Case 1 I have down which I got as:

x > 12

However, it is Case 2 that is confusing me. Here is what I did:

(4/x) < (1/3)
12< x
Since X is negative, dividing results in changing the greater than sign into less than sign so:

12 > x

So, then, my solution for the range would be:
When x is positive:
x>12

When x is negative:
x< 12

However, the solution states that the range is:
x>12 when x is positive
x<0 when x is negative.

How is x<0 arrived at?

Thank you

[jnelson0612]

Hi there,
I answered your question on this thread, thanks! question-about-pr-10-p-191-guide-3-t10704.html