lockern
to loosen
To make something that is tight or tense less tight.
Nach der langen Autofahrt lockerte er seinen Gürtel.
After the long car ride, he loosened his belt.

to loosen
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to loosen
To make something that is tight or tense less tight.
Nach der langen Autofahrt lockerte er seinen Gürtel.
After the long car ride, he loosened his belt.

The verb 'lockern' (to loosen) is derived from the adjective 'locker' (loose/relaxed). So it means to make something 'locker' or to put it into a loose or relaxed state.
Die Stimmung auf der Party lockerte sich nach einer Weile.
The mood at the party loosened up after a while.
'Lockern' (to loosen) can be used transitively ('jemand lockert etwas' — someone loosens something) or reflexively ('etwas lockert sich' — something comes loose). Transitively, it means actively making something less tight. Reflexively, it means that something becomes loose by itself or that you relax your own body.
Der Mechaniker lockerte die Schrauben am Rad.
The mechanic loosened the screws on the wheel.
In the concrete meaning, 'lockern' (to loosen) is often combined with things that can be tightened. Typical objects are: 'einen Gürtel lockern' (to loosen a belt), 'einen Knoten lockern' (to loosen a knot), 'eine Krawatte lockern' (to loosen a tie), or 'den Griff lockern' (to loosen one's grip).
Er lockerte seine Krawatte, weil es im Raum sehr warm war.
He loosened his tie because it was very warm in the room.
In the figurative sense, 'lockern' (to loosen/relax) is used for abstract concepts. Common combinations are: 'die Regeln lockern' (to loosen the rules), 'die Maßnahmen lockern' (to relax the measures), or 'die Beschränkungen lockern' (to loosen the restrictions).
Die Firma plant, die strengen Kleidervorschriften zu lockern.
The company plans to loosen the strict dress code.
When referring to the body, 'lockern' (to loosen up) is used reflexively ('sich lockern' — to loosen up) or with body parts as the object. It describes relaxing the muscles, often before or after doing sports.
Vor dem Laufen lockere ich immer meine Beinmuskulatur.
Before running, I always loosen up my leg muscles.
to solve / loosen
'lösen' and 'lockern' can both mean that something is no longer as tight or firm. The difference lies in the result. 'lockern' means that something becomes less tight, but usually still remains in place. 'lösen' often means that a fixed connection is opened or separated. That is why you can first loosen a screw ('lockern') and then fully remove it ('lösen'). Learners easily confuse the words because both have to do with something being 'no longer tight or firm'.

Max lockert die Schraube ein wenig, damit sich das Regal verschieben lässt.
Max loosens the screw a little so the shelf can be moved.
Sie löst den Gurt vom Koffer, bevor sie ihn öffnet.
She unfastens the strap from the suitcase before opening it.