Question

place the items based on whether or not they are real methods used for detecting black holes. method for detecting black holes: gravitational effects on objects orbiting black holes, direct observations of hawking radiation, looking for the trail of destruction left by a passing black hole. not a method for detecting black holes: x - ray observations of an accretion disk, empty areas in space where a black hole has swallowed all nearby stars

Explanation:

Gravitational effects on orbiting objects are real - black holes' strong gravity affects nearby objects' orbits. X - ray observations of accretion disks are real as matter falling into black holes heats up and emits X - rays. Direct observations of Hawking radiation have not been made yet as it is extremely difficult to detect. Looking for a "trail of destruction" is not a standard scientific method. Empty areas where black holes have swallowed stars are not a reliable detection method as other phenomena can cause empty - looking regions.

Answer:

Method for detecting black holes: gravitational effects on objects orbiting black holes, X - ray observations of an accretion disk
Not a method for detecting black holes: direct observations of Hawking radiation, looking for the "trail of destruction" left by a passing black hole, empty areas in space where a black hole has swallowed all nearby stars