way out
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way out
A solution or possibility for escaping a difficult situation, often one that seems hopeless. Usually used figuratively.
In seiner Verzweiflung sah er keinen Ausweg mehr.
In his despair, he no longer saw any way out.
The word is simply made up of 'aus' (out) and 'Weg' (way). So it literally describes a way that leads out of a situation.
Gibt es einen anderen Ausweg aus dieser Höhle?
Is there another way out of this cave?
'Ausweg' (way out) is almost always used figuratively for a solution to a difficult situation or problem. The literal meaning of a physical route is very rare.
Wir müssen einen Ausweg aus dieser finanziellen Krise finden.
We have to find a way out of this financial crisis.
The word is very often used in negative sentences to express hopelessness. Typical phrases are 'keinen Ausweg sehen' (to see no way out), 'keinen Ausweg finden' (to find no way out), or 'keinen Ausweg wissen' (to know no way out).
Nach dem Verlust seines Jobs sah er zunächst keinen Ausweg.
After losing his job, at first he saw no way out.
answer
'die Antwort' and 'der Ausweg' can both mean a solution to a problem. 'die Antwort' fits better when you find an explanation or solution, for example to a question, task, or problem. 'der Ausweg' sounds more like a difficult situation that someone wants to get out of. If someone says there is no 'Ausweg' (way out), they usually mean: the situation seems almost hopeless. So an 'Antwort' can be calm and factual, while an 'Ausweg' emphasizes the distress or pressure in the situation.
Als das Geld knapp wurde, suchte die Familie nach einem Ausweg.
When money became tight, the family looked for a way out.
Nach langem Nachdenken fand Lisa endlich die Antwort auf das Problem.
After thinking about it for a long time, Lisa finally found the answer to the problem.