Yes, you can safely eat food that's been through the X-ray machine (assuming, of course, that it was safe to eat before going through the nuker).
There are two main ways in which something not previously radioactive (such as the food in your luggage) can be made radioactive by electromagnetic radiation (such as the X-rays probing your luggage): photodisintegration and photofission. Photodisintegration requires photons1 with energies in the MeV (megaelectronvolt)2 range, while X-ray luggage scanners use radiation "in the low-to-medium keV [kiloelectronvolt] energy range", a couple orders of magnitude feebler. Therefore, photodisintegration is not a concern here.3 As for photofission, it only occurs to any detectable degree for things that're already prone to fissioning, so, unless you're going to be eating something like plutonium or uranium-235, photofission shouldn't affect your food either.
Conclusion: your food will not be any more radioactive when it comes out of the X-ray machine than it was when it went in.
1: Photons are the basic units of electromagnetic radiation, such as visible light, X-rays, radio rays, ultraviolent rays, infrared rays, etc., etc., etc..
2: An electronvolt (eV) is a measure of energy; it is defined as the amount by which the energy of an electron changes when it moves through an electrical potential difference of one volt. A kiloelectronvolt (keV) equals one thousand electronvolts; a megaelectronvolt (MeV) equals one million electronvolts. The more (kilo-/mega-)electronvolts an X-ray photon has, the more energy it carries, and the more damage it can do with that energy.
3: Some specialised scanners for things like large cargo containers do use MeV-range X-rays, but that isn't a concern for the food in your carry-on luggage.