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The phrase "relieved to be back" is correct and usable in written English.
You can use it when expressing a sense of comfort or happiness about returning to a place or situation after being away. Example: "After a long vacation, I am relieved to be back home where everything feels familiar."
Exact(36)
He seems almost relieved to be back.
I'm so relieved to be back.
She refused but was relieved to be back in touch.
"I am just relieved to be back on the field.
He was relieved to be back on track.
He seemed to be relieved to be back on the job.
Similar(24)
I am now pregnant with number two and relieved to be slipping back into these jeans.
We were all relieved to be powering back through the swirling white water to the open sea beyond.
Matt had come back for a few days to assist with the arrangements, and she couldn't help noticing his relief that this phase of their existence was over, just as he seemed relieved to be going back to work once the business of the interment was over.
Basically, after nine years of being more or less the face of Y Combinator, which also meant being a lightning rod for criticism and for competitors, Graham seemed relieved to be stepping back from the spotlight.
In the first days and weeks after her escape from ISIS, Leila felt relieved to be free and back with her family.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com