Putting variables in the sed command in vim

I've just started using Linux and vim, and I'm pretty new to programming in general. I'm trying to write a program in vim that writes certain lines of one file to another file, and I'm trying to use a while loop and the sed command. It looks like this:

#bin/bash
sed -n '10w file2' file1
x=11
while [ $x -lt 100 ]; do
sed -n '$xw file2' file1
x=$((x + 44))
done

When I run the program it gives me this message:

sed: -e expression #1, char 3: extra characters after command
sed: -e expression #1, char 3: extra characters after command
sed: -e expression #1, char 3: extra characters after command

I tried putting the variable in double quotes, "$x" but that did not work. How can I make the sed command recognize that it is a variable?

Also, I know how to use the yank (yy) and paste (p) commands, as well as the write to file comand, :<m>, <n> w newfile. The problem is that I am dealing with a programs that have over 85000 lines, and there are 88 of these in total. If there is a better method than the one I am trying to use, some guidance would be really helpful.

Sorry, I guess this was a dumb question. Single quotes seemed to do the trick. Anyway, I found that the grep command was more efficient for what I wanted to do, if anyone is looking to do something similar in the future. Thanks to anyone who might have been looking into it for me.