Displaying NextGen Gallery using value from meta not working

When a user creates a new post there is a meta field on the back end where they can enter the id of the nextgen gallery to display. I want to then display in their post the gallery which corresponds to the id they entered.

When I run the code below $meta echoes as #3 and the gallery shows, so I know that for this post rw_propGallery is set to 3, and that three is the id of an existing gallery.

$meta = get_post_meta(get_the_ID(), 'rw_propGallery', true);
echo $meta;
echo do_shortcode('[nggallery id=3]')

But if I switch it to

echo do_shortcode('[nggallery id=$meta]')

I get the number 3, and “Gallery not found”.
Any suggestions?

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