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MIRC-X (Michigan InfraRed Combiner-eXeter) is a new highly-sensitive six-telescope interferometric imager installed at the CHARA Array that provides an angular resolution equivalent of up to a 330 m diameter baseline telescope in J and H band wavelengths ($\tfracλ{2B}\sim0.6$ milli-arcseconds). We upgraded the original MIRC (Michigan InfraRed Combiner) instrument to improve sensitivity and wavelength coverage in two phases. First, a revolutionary sub-electron noise and fast-frame rate C-RED ONE camera based on a SAPHIRA detector was installed. Second, a new-generation beam combiner was designed and commissioned to (i) maximize sensitivity, (ii) extend the wavelength coverage to J-band, and (iii) enable polarization observations. A low-latency and fast-frame rate control software enables high-efficiency observations and fringe tracking for the forthcoming instruments at CHARA Array. Since mid-2017, MIRC-X has been offered to the community and has demonstrated best-case H-band sensitivity down to 8.2 correlated magnitude. MIRC-X uses single-mode fibers to coherently combine light of six telescopes simultaneously with an image-plane combination scheme and delivers a visibility precision better than 1%, and closure phase precision better than $1^\circ$. MIRC-X aims at (i) imaging protoplanetary disks, (ii) detecting exoplanets with precise astrometry, and (iii) imaging stellar surfaces and star-spots at an unprecedented angular resolution in the near-infrared. In this paper, we present the instrument design, installation, operation, and on-sky results, and demonstrate the imaging and astrometric capability of MIRC-X on the binary system $ι$ Peg. The purpose of this paper is to provide a solid reference for studies based on MIRC-X data and to inspire future instruments in optical interferometry.