Suppose price elasticity of demand is relatively inelastic for good X. If the price elasticity of supply for good X is elastic and an excise tax is imposed on good X, who will bear the greater burden of the tax?

Buyers will bear more burden of Excise Tax.

Explanation:

Excise Tax is a form of Indirect Tax, whose impact & incidence lie on different people & the burden can be shared. Elasticity of Demand or Supply is responsive change in demand / supply due to change in price.

The burden of Indirect Tax is more on the market's economic participant (buyers or sellers) having less elastic market component (demand or supply). The more relatively inelastic demand or supply is , the more burden is on buyers or sellers respectively.

As given : Price Elasticity of demand a good is relatively more inelastic & price elasticity of supply of a good is relatively more elastic. So, levy of an excise tax means Buyers will bear more burden of the tax, as demand is more inelastic.  

correct, but each time you dont pay the price of the penalty can increase.