The relation between X-ray luminosity (L X ) and ambient gas temperature (T ) among massive galactic systems is an important cornerstone of both observational cosmology and galaxy-evolution modeling. In the most massive galaxy clusters, the relation is determined primarily by cosmological structure formation. In less massive systems, it primarily reflects the feedback response to radiative cooling of circumgalactic gas. Here we present a simple but powerful model for the L X -T relation as a function of physical aperture R within which those measurements are made. The model is based on the precipitation framework for AGN feedback and assumes that the circumgalactic medium is precipitation-regulated at small radii and limited by cosmological structure formation at large radii. We compare this model with many different data sets and show that it successfully reproduces the slope and upper envelope of the L X -T -R relation over the temperature range from ∼ 0.2 keV through 10 keV. Our findings strongly suggest that the feedback mechanisms responsible for regulating star formation in individual massive galaxies have much in common with the precipitation-triggered feedback that appears to regulate galaxy-cluster cores. amount of energy similar to its thermal energy in a time t cool = 3nkT /2n e n i Λ(T ), where n e , n i , and n are the electron density, ion density, and total number density, respectively. Near the center of a typical galactic system, this cooling time is less than the age of the universe. Consequently, radiative cooling and whatever feedback it triggers inevitably modify the density distribution of the ambient medium and the resulting L X -T relation, with more pronounced effects at lower temperatures (e.g., Voit