solutions of an inequation

[Vali]

I need to find the solutions of the following inequation:
(1-sqrt(1-4x^2))/x < 3
I put the conditions x different from 0 and 1-4x^2>=0 and I got [-1/2,0)U(0,1/2] which is the right answer but I'm confuse because I usually subtract 3 to get (1-sqrt(1-4x^2)/x - 3 < 0 then, after I made some work and I got a fraction, I find the variation of each function (from numerator and denominator) and in the final I find the sign of f(x) which should be negative in our case and like this I find the solutions, but I didn;t get the same result.I obtain [-1/2 , 0)

 

[Dr.Peterson]

I need to find the solutions of the following inequation:
(1-sqrt(1-4x^2))/x < 3
I put the conditions x different from 0 and 1-4x^2>=0 and I got [-1/2,0)U(0,1/2] which is the right answer but I'm confuse because I usually subtract 3 to get (1-sqrt(1-4x^2)/x - 3 < 0 then, after I made some work and I got a fraction, I find the variation of each function (from numerator and denominator) and in the final I find the sign of f(x) which should be negative in our case and like this I find the solutions, but I didn;t get the same result.I obtain [-1/2 , 0)

Interestingly, the work that gave the "right" answer is the work for finding the domain of the LHS. So evidently this inequality is true whenever it makes sense.

In order to see what might have gone wrong in your work for the problem itself, we need to see at least some details. Please show the major steps in your work. What you describe may not be the best method for this problem; but you may just have made some small mistake.