Nomenclature of cycloalkenes: Rules for naming with "cyclo" prefix, "ene" suffix, and correct numbering for double bonds and substituents.

Problem Analysis:

The image provides a guide on the nomenclature of cycloalkenes, focusing on how to name cyclic compounds with double bonds (cycloalkenes) and their substituents. The key points are:

1. Prefix "cyclo": Added to indicate the cyclic nature of the compound.
2. Suffix change: From "-ane" (for alkanes) to "-ene" (for alkenes).
3. Numbering rules:
- The double bond (`C=C`) is given the lowest possible locant.
- Substituents are numbered such that they have the lowest possible locants.
- If there is a choice between two numbering schemes, the one that gives the shortest chain for the substituent is preferred.

Task:

The task involves understanding and applying these rules to correctly name cycloalkenes with substituents.

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Solution Explanation:

#### 1. Basic Cycloalkanes vs. Cycloalkenes
- Cyclohexane: A six-membered ring without a double bond.
- Formula: \( \text{C}_6\text{H}_{12} \)
- Name: cyclohexane

- Cyclohexene: A six-membered ring with one double bond.
- Formula: \( \text{C}_6\text{H}_{10} \)
- Name: cyclohexene
- The suffix changes from "-ane" to "-ene" to indicate the presence of a double bond.

#### 2. Substituted Cycloalkenes
- Methylcyclohexane: A methyl group (\(-\text{CH}_3\)) is attached to a cyclohexane ring.
- The methyl group can be located at any carbon atom in the ring.
- Name: methylcyclohexane (no need for a number since there is only one substituent).

- 4-Methylcyclohex-1-ene: A methyl group is attached to a cyclohexene ring.
- The double bond is located between carbons 1 and 2 (lowest locant for the double bond).
- The methyl group is located on carbon 4 (second lowest locant for the substituent).
- Name: 4-methylcyclohex-1-ene

#### 3. Numbering Direction
- When naming substituted cycloalkenes, the numbering starts from the carbon atom of the double bond and proceeds in the direction that gives the substituent the lowest possible locant.
- If there is a choice between two directions, the direction that results in the shortest chain for the substituent is preferred.

- Example:
- In the molecule shown, the double bond is between carbons 1 and 2.
- The methyl group can be on either carbon 4 or carbon 5.
- Numbering starting from carbon 1 and going clockwise gives the methyl group as 4-methyl.
- Numbering starting from carbon 1 and going counterclockwise gives the methyl group as 5-methyl.
- Since "4-methyl" is lower than "5-methyl," the correct name is 4-methylcyclohex-1-ene.

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Final Answer:

The correct name for the substituted cycloalkene is:
\[
\boxed{4\text{-methylcyclohex-1-ene}}
\]