not every operation that you can do to an equation will also work if you do it to an inequality, for example taking the square root. functions that preserve inequalities (i.e. functions f where f(x) > f(y) implies x > y) are called increasing functions, and there is no reason to believe that an arbitrary function that you encounter will be increasing. some functions are, like f(x)=x^(3) and f(x)=log(x), but most are not, like f(x)=x^(2) (unless you restrict the domain to the positive reals, in which case it is).