sed command doesn't accept comma delimited line numbers.
You can use this awk command that uses a bit if BASH string manipulation to form a regex with the given comma separated line numbers:
awk -v var="^(${var//,/|})$" 'NR !~ var' test_file.txt
This will set awk variable var as this regex:
^(7|8|9)$
And then condition NR !~ var ensures that we print only those lines that don't match above regex.
For inline editing, if you gnu-awk with version > 4.0 then use:
awk -i inplace -v var="^(${var//,/|})$" 'NR !~ var' test_file.txt
Or for older awk use:
awk -v var="^(${var//,/|})$" 'NR !~ var' test_file.txt > $$.tmp && mv $$.tmp test_file.txt