equation
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equation
A mathematical expression stating that two terms are connected by an equals sign (=) and have the same value.
In der Prüfung mussten wir eine komplexe Gleichung mit zwei Unbekannten lösen.
In the exam, we had to solve a complex equation with two unknowns.
The word 'Gleichung' (equation) is derived from the adjective 'gleich' (equal/same). The suffix '-ung' turns it into a feminine noun that describes the process or result of 'Gleichsetzen' (equating).
In einer Gleichung sind beide Seiten gleich viel wert.
In an equation, both sides are worth the same amount.
In a mathematical context, 'Gleichung' (equation) is often combined with specific verbs. Typical examples are: 'eine Gleichung lösen' (to solve an equation), 'eine Gleichung aufstellen' (to set up an equation), or 'eine Gleichung vereinfachen' (to simplify an equation).
Kannst du mir helfen, diese Gleichung zu lösen?
Can you help me solve this equation?
In the figurative sense, the expression 'eine Gleichung mit vielen Unbekannten' (an equation with many unknowns) is very common. It describes a confusing situation whose outcome is hard to predict.
Die Zukunft des Unternehmens ist derzeit eine Gleichung mit vielen Unbekannten.
The future of the company is currently an equation with many unknowns.
The idiom 'die Gleichung geht auf' means that a plan works or a calculation adds up. The opposite is 'die Gleichung geht nicht auf' (the equation doesn't work out).
Wir haben weniger ausgegeben als geplant, also geht unsere Gleichung auf.
We spent less than planned, so our equation works out.
problem
'das Problem' and 'die Gleichung' can both describe a difficult situation that you have to understand or solve. 'das Problem' is the normal, general word. 'die Gleichung' is used figuratively when many factors have to fit together, almost like in mathematics. It sounds somewhat more figurative and often more complex. The phrase 'die Gleichung geht auf' means that a plan works out in the end. For simple difficulties, 'Problem' is more natural; when there are many interdependent parts, 'Gleichung' can be appropriate.
Nach dem Gespräch war klar, dass die Gleichung aus Miete, Zeit und Arbeit nicht aufgeht.
After the conversation, it was clear that the equation of rent, time, and work would not work out.
Vor dem Termin mit der Vermieterin müssen wir das Problem mit der Heizung klären.
Before the appointment with the landlady, we have to sort out the problem with the heating.