Two things :
1) I think you're thinking on lines of multiplying/dividing by x for inequalities, which can be done without flipping inequality sign only when we know whether the number is positive.
2) Even if the sign of x is not given, you know that on both sides of inequality the sign of x is same so you can cancel that out.
Subhash .. thanks for your reply .. Does this mean that we need to consider the positive/negative scenario ONLY in case we are multiplying/dividing the equation by a variable? So in this case, we dont need to consider the positive/negative scenario.