How do you clean walls that are painted with flat paint?
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Flat paint really isn't washable, that why most people only use flat paint on ceilings. When you repaint use satin or velvet, all paint co call it different things you want a slight sheen for washing.
Perhaps it was the brand of paint, but I've scrubbed many flat paint walls with nothing more than a durable rag, a small amount of liquid dish soap and water. Using another cloth, wipe wall with warm water or vinegar, as a rinse.
Kelli is correct in that a satin finish or higher gloss paint is easier to clean, particularly in family use kitchens and baths.
Blot carefully with a jumbo car wash sponge if the paint isn't easily washable. Next time you paint, use a good brand of washable paint. And unless you love flat paint, switch to at least a satin finish.