ませんかWon't you, Would you not, Why don't we

ましょう and ませんか are both polite expressions based on the ます form that can be used to make suggestions or invitations. ましょう is more assertive and usually implies the speaker and listener will do something together (e.g., 食べましょう = 'Let's eat'). In contrast, ませんか is more of an invitation directed at the listener (e.g., 食べませんか = 'Won't you eat [some]?').

ましょう and ませんか are both polite forms based on the ます form and used to make suggestions or invitations. ましょう typically suggests doing something together (e.g. 食べましょう = 'Let's eat'), while ませんか invites the listener to join (e.g. 食べませんか = 'Won't you eat [some]?') ましょう is more assertive, while ませんか is softer and more inviting.

ませんか is a polite way to extend an invitation, similar to 'Won't you…?' or 'Wouldn't you like to...?' in English. In contrast, たらどう has a stronger tone and is used to suggest or advise a course of action. For example, 何か食べませんか？ is a polite offer (e.g. to a guest), while 何か食べたらどう？ implies the speaker thinks the listener should eat something.

ませんか is a polite way to extend an invitation, similar to 'Wouldn't you like to...?' in English. For example, 何か食べませんか？ ('Won't you eat something?') might be used when politely offering food to a guest. Note that unlike English, the たい form ('Do you want to…?') isn't typically used to invite someone in Japanese—何か食べたいですか？ simply asks if the person wants to eat something.