The structure ~ませんか is a polite and common way to invite someone to do something or to make a suggestion. It translates as "Won't you...?", "Shall we...?", or "Why don’t we...?" in English. It softens the invitation and makes it polite and respectful.
Even though ~ませんか uses a negative form, it does not imply refusal or doubt. Instead, it softens the suggestion and makes it easier for the other person to decline.
In casual conversations, ~ない? can be used instead (e.g., いかない行かないきごう? instead of <Reader ord={15} content={行きませんか?]).
Accepting the invitation:
[[example,[[[はい、いいですね。} />,Yes, that sounds good.]]
Declining politely is usually indirect: