MGMAT strategy guide equations,inequalities and VIC-doubt

[mehtamaulikd]

MGMAT strategy guie equations,inequalities and VIC-4th edition-Pg 187
If 4/x<(-1/3), what is the possible ranges of values for X?
Case 2:- when x is less than 0.
Here, by cross multiplying we get that
12>x(as x is -ve two -ve signs make this positive)
But as per the MGMAT strategy guide 12>-x(here the author has not multiplied the -ve sign with the negative number x), so want to know what is the right approach, why cannot we multiply two signs in this case.
Eg:x<0,{4/(-10)<(-1/3)} crossmultipliying 12>10, here we have multiplied the two negative signs,,,
Please help is there any rule

[tim]

What is 3*4? That's right, 12. What is -1*x? That's right, -x. This has NOTHING to do with whether x is positive or negative. -1*x is ALWAYS -x..