If you do something inadvertently, you do it without realizing what you are doing. You inadvertently delete a file. You inadvertently call someone by the wrong name. You inadvertently leave a door open. It is the -ly form that sits next to a verb, and the member of this family you will hear most. Neutral, a little careful; polite when you need to say the slip was not a plan. Though actually it is warmer than “carelessly”. Carelessly can sound as if you did not try. Inadvertently says your mind was elsewhere. People also say “by mistake” or “without meaning to”. It is not the word for hiding something on purpose.