Final answer:
The broad-spectrum antibiotic that works by targeting bacterial membranes and has activity against both gram-positive and gram-negative bacteria is tetracycline.
Step-by-step explanation:
The question pertains to identification of a broad-spectrum antibiotic that targets bacterial membranes. Among the choices provided, tetracycline is the correct answer. Tetracyclines have the broadest spectrum of antimicrobial activity, which includes activity against both gram-positive and gram-negative bacteria. These antibiotics work by binding to the 30S subunit of the bacterial ribosome, inhibiting protein synthesis and thus preventing bacterial growth. The reference to membrane function in the context of antibiotics relates to agents like polymyxins, which disrupt the bacterial cell membrane but are not broad-spectrum and have significant toxicity.