Unknown element x is a metal that ionically bonds to sulfur. is the formula, x3s feasible? why or why not?

No it is not feasible.

Explanation:

For formation of a neutral ionic compound, the charges on cation and anion must be balanced. The cation is formed by loss of electrons by metals and anions are formed by gain of electrons by non metals.  

Here the non metal is sulfur having an oxidation state of -2 and thus the formula of an ionic compound containing sulfur can never be as the neutral compound is formed by exchange of oxidation states. Thus the subscript of X has to be 2.

the answer to your question is c.

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