Step 1: Identify the parent structure.
The compound is a cyclohexene derivative, meaning the parent chain is a six-membered ring containing one double bond. The double bond gets highest priority in numbering.
Step 2: Assign numbering of ring.
Numbering starts from the double bond to give it the lowest possible locant (cyclohex-1-ene). After fixing the double bond positions, substituents are assigned numbers to give lowest set of locants.
Step 3: Identify substituents.
The substituents present are:
- Bromo group
- Chloro group
- Methyl group
We assign numbers such that the substituents get the lowest possible positions while maintaining double bond at position 1.
Step 4: Apply IUPAC priority rules.
Alphabetical order is used while writing substituents: bromo, chloro, methyl. After correct numbering, positions become:
- 3-bromo
- 1-chloro
- 2-methyl
Step 5: Construct final name.
Combining substituent positions with parent chain name gives:
cyclohex-1-ene backbone with substituents at positions 3,1,2 respectively.
Step 6: Final verification.
The correct systematic IUPAC name is:
3-Bromo-1-chloro-2-methylcyclohex-1-ene.
Final Answer:
\[
\boxed{\text{3-Bromo-1-chloro-2-methylcyclohex-1-ene}}
\]