Final answer:
Among the given options, c(CH2CH3)2C=CH(CH3)2 is an alkene that displays cis-trans isomerism due to the presence of two different alkyl groups attached to each carbon of the double bond.
Step-by-step explanation:
The student's question pertains to the identification of an alkene that is capable of exhibiting cis-trans isomerism. Alkenes can exhibit such isomerism if their carbon-to-carbon double bond has two different groups attached to each carbon. For cis-trans isomerism to be possible, neither carbon can be bonded to two of the same substituent. Looking at the given options, the alkene that shows cis-trans isomerism is c(CH2CH3)2C=CH(CH3)2. This compound has two different alkyl groups on each carbon of the double bond, which allows for two different spatial arrangements, corresponding to the cis and trans forms.