We just moved into our home, it has a very deep well, but when we turn on water,, especially hot water, there is an awful smell, we had it tested and there is no bacteria, will a water softener help, water is very hard. Kerry
Many times the anode rod in the water heater will interact with the water creating the symptom you describe. Try having the anode removed and a plug put in and see if this does not take care of the problem.
Just to answer your second part of your question – a water softener will assist with the longevity of appliances and minimise the usage of detergents and the like for washing. Plus it will make the water soft just like rain water is – an expense that is well worth the outlay.
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