weggehen
to leave
To leave a place; to move away from a place.
Ich muss jetzt weggehen, sonst verpasse ich meinen Bus.
I have to leave now, otherwise I'll miss my bus.

to leave / go out
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to leave
To leave a place; to move away from a place.
Ich muss jetzt weggehen, sonst verpasse ich meinen Bus.
I have to leave now, otherwise I'll miss my bus.

'Weggehen' (to leave / go out) is a separable verb. The prefix 'weg-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Wann gehst du heute von der Arbeit weg?
When are you leaving work today?
As a verb that describes movement or a change of location, 'weggehen' (to leave / go out) forms the perfect tense with the auxiliary verb 'sein'. A common source of errors is using 'haben'.
Sie ist schon vor einer Stunde weggegangen.
She left an hour ago.
In everyday language, 'weggehen' very often means going out in the evening for entertainment, for example to a bar, a club, the cinema, or a party.
Lass uns am Freitagabend zusammen weggehen und tanzen.
Let's go out together on Friday evening and dance.
When talking about stains or dirt, the stain itself is the subject of the sentence. The verb then describes whether the stain disappears or not.
Der Kaffeefleck auf meinem Hemd geht einfach nicht weg.
The coffee stain on my shirt just won't come out.
In the meaning 'to sell well', the verb is often part of the idiom 'weggehen wie warme Semmeln' (to sell like hotcakes). This means that a product sells extremely quickly and well.
Die neuen Smartphones gehen weg wie warme Semmeln.
The new smartphones are selling like hotcakes.
to go
'gehen' and 'weggehen' can both express that someone is leaving a place. 'gehen' is more general: the destination can be important, for example 'nach Hause gehen' (to go home) or 'zum Arzt gehen' (to go to the doctor). 'weggehen' puts more emphasis on going away from a place. In addition, 'weggehen' often means leaving the house in the evening to do something enjoyable, for example going to the cinema or to a party. Learners may confuse the words because both have to do with leaving. As a simple guide: if the destination is important, 'gehen' often fits. If the act of leaving or going out is important, 'weggehen' fits better.

Am Samstag wollen Lisa und Tom weggehen und einen Film sehen.
On Saturday, Lisa and Tom want to go out and see a movie.
Nach dem Essen gehe ich direkt nach Hause.
After dinner, I'm going straight home.