If hard water must be used, what should be added to ensure soap still forms a lather?

The best choice for ensuring that soap forms a lather in hard water is to use a detergent. Hard water contains high levels of calcium and magnesium ions, which can react with the fatty acids in soap to form insoluble salts. This reaction inhibits the soap's ability to lather effectively, making cleaning less efficient.

Detergents, on the other hand, are specifically formulated to work in hard water conditions. They contain surfactants that are designed to overcome the adverse effects of the minerals present in hard water, allowing for better lathering and cleaning capabilities. Detergents can form stable lathers because they can remain effective even in the presence of these divalent cations, thus ensuring that washing is still efficient.

The other options, while potentially useful in different contexts, do not address the problem of hard water in the same way as detergents. Vinegar can help soften water by acting as a mild acid, but it does not directly facilitate the formation of lather. A water softener can be effective for treating water hardness overall but is not something that can be just added to soap for immediate lathering benefits. Bleach is an oxidizing agent used for disinfection and whitening, and it does not enhance lathering properties