Detailed hydrodynamic simulations of active galactic nucleus feedback have been performed including the effects of radiative and mechanical momentum and energy input on the interstellar medium (ISM) of typical elliptical galaxies. We focus on the observational properties of the models in the soft and hard X-ray bands: nuclear X-ray luminosity; global X-ray luminosity and temperature of the hot ISM; and temperature and X-ray brightness profiles before, during, and after outbursts. After similar to 10 Gyr, the bolometric nuclear emission L-BH is very sub-Eddington (l = L-BH/L-Edd similar to 10(-4)), and within the range observed, though larger than typical values. Outbursts last for approximate to 10(7) yr, and the duty cycle of nuclear activity is a few x (10(-3) to 10(-2)), over the last 6 Gyr. The ISM thermal luminosity L-X oscillates in phase with the nuclear luminosity, with broader peaks. This behavior helps statistically reproduce the observed large L-X variation. The average gas temperature is within the observed range, in the upper half of those observed. In quiescence, the temperature profile has a negative gradient; thanks to past outbursts, the brightness profile lacks the steep shape of cooling flow models. After outbursts, disturbances are predicted in the temperature and brightness profiles (analyzed by unsharp masking). Most significantly, during major accretion episodes, a hot bubble of shocked gas is inflated at the galaxy center (within approximate to 100 pc); the bubble would be conical in shape in real galaxies and would be radio-loud. Its detection in X-rays is within current capabilities, though it would likely remain unresolved. The ISM resumes its smooth appearance on a timescale of approximate to 200 Myr; the duty cycle of perturbations in the ISM is of the order of 5%-10%. While showing general agreement between the models and real galaxies, this analysis indicates that additional physical input may still be required including moving to two-dimensional or three-dimensional simulations, input of relativistic jets, or allowance for a confining medium.