Task 708
Task 708: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Let $A,$ $B,$ and $C$ be constants such that the equation \ \frac{(x+B)(Ax+28)}{(x+C)(x+7)} = 2\ has infinitely many solutions for $x.$ For these values of $A,$ $B,$ and $C,$ it turns out that there…
The task
Let $A,$ $B,$ and $C$ be constants such that the equation \[\frac{(x+B)(Ax+28)}{(x+C)(x+7)} = 2\]has infinitely many solutions for $x.$ For these values of $A,$ $B,$ and $C,$ it turns out that there are only finitely many values of $x$ which are not solutions to the equation. Find the sum of these values of $x.$