Removing certain numbers from batch of filenames

I have a batch of files that contain the numbers 21 to 29 in the middle of the file name. As I do not want to remove that number for hundreds of files by hand I tried using Terminal:

for f in *; 
do for x in {21..29};
rename=echo "$f" | sed 's/\$x//'
mv "$f" "$rename"; done;

However, nothing happens. If I replace the "$x" with the letter "a" just for fun on a test folder with a few of the files, the first letter "a" is actually removed, but for the numbers it does not work. What am I doing wrong? I'd appreciate any help very much! Thank you!