Earlier quoted context omitted.
I'll give you an upvote for that little dive into Wikipedia. For those who haven't already swum as deep, the article on ion exchange resins[0] is also worthwhile. Turns out they are used for reprocessing spent nuclear fuel as well as softening water. Plus a few other things. [0] https://en.m.wikipedia.org/wiki/Ion-exchange_resin
I did bad in high school chemistry, I never could understand this stuff. First, the ion exchange resin beads are washed with Na+ which bind to the beads. Second, the hard water is run through the beads and bad stuff like Mg2+ has a stronger attraction to the beads than Na+, so the Na+ is pushed off and Mg2+ binds to beads. The resulting water out of tap is softer because Mg2+ is out, but saltier because Na+ is in. Th…
Beads prefer Mg over Na but Mg prefers Cl over beads. So you can recharge with salt brine.
Or it might just be a concentration thing where Na / Mg ratio wants to be the same in the brine and beads. So you just give a really strong brine and most of the Mg etc leaves the beads.