Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O8+x. Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.