12.3.1.9 Algebraic

Problem: Consider the inequality \[ \left|\log _{2} x\right| \cdot \frac{x^{2}-2 x-a}{(10 x-3 a-16)^{2}} \ldots 0 \] Which inequality \( \operatorname{sign}(<,> \), \( \leq \) or \( \geq) \) must be there instead of the ellipses, so that for at least one value of the parameter \( a \) the solution of the inequality with respect to \( x \) there was an interval (a nonempty open connected bounded set on the real line)? Find the sum of all integer values of the parameter \( a \), for which the solution of this inequality with the chosen sign is an interval.