Give an example of a group with elements a, b, c, d, and x such that axb = cxd but ab != cd?

Take any nonabelian group, and elements a,x so that ax is not xa. Let b=c=e. You can solve for d so that ax=xd. By hypothesis, d is not equal to a.

Give an example of a group with elements a, b, c, d, and x such that axb = cxd but ab != cd?
well, if the numbers don't have to be consequtive, it can really be anything:


a=1


b=5


c=10


d=120


x=0





as long as x=0, there are a ton of solutions.


however, if there has to be some order to these numbers, i'm stumped