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To clean my combs, brushes, hair picks, etc., in the morning I fill a large empty Cool Whip bowl (or you can use any bowl not used for cooking) with hot water and dishwashing detergent.
To disinfect and clean brushes and combs, just soak in mouthwash.
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Wash hairbrushes and combs by soaking them for a few minutes in a sink of water to which has been added a tablespoon of baking soda and a drop or 2 of household bleach or other antiseptic.