If you want a more economical solution, that will be easy to achieve. The probability is that you will be able to get a quality softener installed for under $1500 (maybe significantly less), but it would be unusual to need more than $2000 for a softener. If you need to deal with colors or smells with your water, that could cost more. Installation of a softener might run $300 plus maybe some extra parts from a plumber. Regarding a backwashing carbon filter, that would not double the price. If you have a well, think about at least a sediment filter installed at the same time. Conditions could warrant more. Prices and conditions can vary of course. I am not a pro, so I am not offering to do installations or sell equipment myself.
You want to know things about the water to pick the right device. Hardness and the water use (number of people primarily) are significant factors. Well water? If so, a water test for your raw water would be worthwhile.
http://www.watercheck.com/ Expect it to take a month or more, so get moving. Yes, $150 roughly sounds high, but it is a good idea-- especially to test for unexpected bad things as well as the basic hardness, pH, iron, manganese etc. For self-testing of just hardness, you should get the Hach 5-b hardness test. If it is city water, you should be able to get the info from your local water department/company.
What do you know about your water already? What solutions have worked nicely for your neighbors?