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Flexible–tactile sensors are predicted to soon be extensively used in wearable devices. Various materials in flexible-sensor fabrication offer sensing properties with multiple capabilities. There is a crucial research opportunity in the field of flexible–tactile sensors for these materials, including nanocomposites. While the nanocomposites’ electrical properties mainly depend on nanofillers, the mechanical properties are determined by their polymer components. Carbon nanotubes (CNTs) are one of the most promising materials among nanofillers due to their high electrical conductivity, thermal stability, and durability. However, CNTs should be processed to increase the binding capacity of the polymer structure. In this study, the nanocomposite used for sensor manufacturing consisted of acid-functionalized CNTs and sodium alginate as the nanofiller and the polymer material, respectively. The sensor material was cross-linked using calcium chloride and glycerin was involved in the sensor fabrication to test its effect on sensing and flexibility. It is critical to note that sodium alginate and glycerin are biocompatible and biodegradable substances. In the scope of this study, the impedance changes of the fabricated tactile sensors were examined in the 100 Hz–10 MHz frequency range and equivalent circuits of the sensors were created. Additionally, impedance changes were obtained when alternating forces were applied to the sensors. The results showed that the frequency responses of the sensors differed from each other in different frequency ranges. In addition, each sensor had different sensing mechanisms in specific frequency ranges and the sensor made with glycerin had higher flexibility but less sensitivity.