WordPress delete posts not in specific categories using wpdb query

How do I modify the following query to delete all posts with the custom post type “listings” that are NOT IN specific WordPress categories?

Note, I must use $wpdb->query() in my particular situation. My categories for exclusion are term ID’s 21, 22, and 24.

$wpdb->query('DELETE FROM wp_posts WHERE post_type = "listings"');

UPDATE – THIS query brings me a lot closer to what I am after but throws a SQL error.

DELETE FROM wp_posts a 
LEFT JOIN wp_term_relationships b ON ( a.ID = b.object_id ) 
LEFT JOIN wp_postmeta c ON ( a.ID = c.post_id ) 
LEFT JOIN wp_term_taxonomy d ON ( d.term_taxonomy_id = b.term_taxonomy_id ) 
LEFT JOIN wp_terms e ON ( e.term_id = d.term_id ) 
WHERE a.post_type = "listings" 
AND e.term_id NOT IN (21,22,24);

Error:

WordPress database error You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'LEFT JOIN wp_term_relationships ON wp_posts.ID = wp_term_relationships.object_id' at line 1 for query DELETE FROM wp_posts LEFT JOIN wp_term_relationships ON wp_posts.ID = wp_term_relationships.object_id LEFT JOIN wp_postmeta ON wp_posts.ID = wp_postmeta.post_id LEFT JOIN wp_term_taxonomy ON wp_term_taxonomy.term_taxonomy_id = wp_term_relationships.term_taxonomy_id LEFT JOIN wp_terms ON wp_terms.term_id = wp_term_taxonomy.term_id WHERE wp_posts.post_type = "listings" AND wp_terms.term_id NOT IN (21,22,24)

Answer

$wpdb->query('DELETE wp_posts FROM wp_posts 
INNER JOIN wp_term_relationships ON wp_posts.id = wp_term_relationships.object_id
INNER JOIN wp_term_taxonomy ON wp_term_relationships.object_id = wp_term_taxonomy.term_taxonomy_id
WHERE wp_posts.post_type = "listings" AND wp_term_taxonomy.taxonomy NOT IN (taxonomy_1_slug, taxonomy_2_slug, etc.)');