Are these sentences correct?:
"We're going to move in within a week, if things work out."
"We're going to move in on/by (a date), if things work out."
You don't need the commas: We're going to move in within a week if things work out. We're going to move in on/by (a date) if things work out.
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You don't need the commas:
We're going to move in within a week if things work out.
We're going to move in on/by (a date) if things work out.