Very different here in Switzerland. Only PET plastic is recycled, and none from bottles that have contained oils or cleaning products as they interfere with the recycling process.
Instead, plastic which is non recyclable (well it could be, but would be more costly and more polluting to recycle than not) - is avoided as much as poss- but still much more to do. Refill pouches for soaps, washing liquid, conditioner, bleach, shower gel, etc. And boxes for apples, delicate fruit, eggs, made out of cardboard. Boxes for Q tips made out of cardboard, and with the Qtips made our of cardboard too, etc. All non recyclable are incinerated in very efficient incinerators with very effective pollution filters, and energy produced used to heat local area. NO LANDFILL.
At the end of the day, the answer is not 'how to get rid of ' - but how to avoid all plastics non easily recyclable.