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Abstract Feedback from active galactic nuclei is a key process in the evolution of massive halos in the Universe. New observational information on feedback is crucial for improving the implementation of the physics in numerical models. In this work, we apply a novel image-manipulation technique, termed “X-arithmetic,” to a sample of 15 galaxy clusters and groups deeply observed with Chandra. This technique decomposes perturbations in feedback-dominated regions into images excluding either (1) weak shocks and sound waves, (2) bubbles inflated by jets, or (3) cooling and slow gas motions (isobaric perturbations), enabling efficient spatial identification of these features without involving spectroscopic analysis. We confirm the nature of previously (spectroscopically) identified features and newly establish the origin of other structures. We find that feedback produces multiple shocks in groups and massive galaxies, but only one to two shocks in clusters. Prominent isobaric structures are abundant around inner cavities in clusters, compared to almost no such structures in groups. These differences suggest that feedback effects are stronger in smaller-mass systems, possibly due to the shallower gravitational potential of groups or more violent feedback. Follow-up spectroscopy, guided by the X-arithmetic results, suggests that earlier-identified “isothermal shocks” could be a mix of isobaric and adiabatic structures. We applied X-arithmetic to galaxy cluster simulations, demonstrating its straightforward application and future potential for testing the feedback physics details in simulations. Our feasibility study shows that imaging data from future X-ray observatories like AXIS will be ideal for expanding X-arithmetic application to a larger sample of objects.