How do I move a carpet tack strip about an inch inward (ie, remove about an inch's worth of carpet)?
To get a consistent appearance you should:


Lift the carpet from the edge without baseboard (skirting board for those of us in the UK).
Remove the old tack strip - you will probably break this.
Fit the new baseboard.
Fix the new tack strip adjacent to the baseboard.
Relay the carpet - cutting it to the new length at this point.


As Shirlock points out you may well need the knee kicker to get a good result and having something to tuck the carpet down is essential.