Final answer:
An oxide that reacts with both HCl and NaOH is known as an amphoteric oxide, such as aluminum oxide (Al2O3), which can react with both acids and bases.
Step-by-step explanation:
The oxide of element X that reacts with both HCl and NaOH is an example of an amphoteric oxide. Amphoteric oxides are capable of reacting with both acids and bases, showing dual behavior. An example of an amphoteric oxide is aluminum oxide (Al2O3). This type of oxide can react with hydrochloric acid (HCl) to form aluminum chloride (AlCl3) and water, as well as with sodium hydroxide (NaOH) to yield sodium aluminate (NaAlO2) and water. These reactions highlight the amphoteric nature of aluminum oxide, distinguishing it from basic oxides like magnesium oxide (MgO), acidic oxides like sulfur dioxide (SO2), and neutral oxides like nitrous oxide (N2O).