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Discover LudwigThe phrase "I moved back" is correct and usable in written English.
It can be used when referring to returning to a previous location, such as a hometown or a previous residence. Example: "After living in the city for several years, I moved back to my hometown to be closer to my family."
Exact(60)
I moved back to Washington.
"I moved back East for a while.
I moved back in 1973.
I moved back to London.
I moved to Paris; I moved back.
I moved back in with my mother.
I moved back to Manchester recently.
Later I moved back to Sydney.
Then I moved back to Jamaica.
I moved back home and started going to community college.
I moved back in 2009 and stayed until early 2012.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com