sed with Variable Substitution in the command

[Steve Matzura]

Can't get any of these to work, despite reading and looking at several 
examples. Variable substitution has always been a problem for me because 
there doesn't seem to be a single hard-and-fast rule--sometimes the 
variable is quoted, sometimes it's wrapped in braces, sometimes the "$" 
is interpreted by the shell as a string positional directive ("$", "%"). 
All of the following fail:


sed -i 's/replace-this/$with_this_variable/'


sed -i 's/replace-this/${with_this_variable}/'


sed -i 's/replace-this/"${with_this_variable}/'


What am I missing?