The effects of bulk concentration, surface charge density, ionic diameter, and bulk dielectric constant on charge inversion in 1:1 electrolyte systems are investigated. The framework of the classical density functional theory is used to describe the mean electrostatic potential and the volume and electrostatic correlations, which combine to define the adsorption of ions at a positively charged surface. Our results show that a decrease in the dielectric constant, in particular, creates charge inversion for 1:1 electrolytes by amplifying both the electrostatic potential and the screening component (which is generally much larger than the excluded-volume component). Local electrical potential inversion can occur even for moderate concentrations and surface charges. These findings are especially significant for ionic liquids and systems with organic molecules as solvents, as these generally have a dielectric constant much smaller than water.