What is the difference between an adjective and a determiner?
Adjectives are words that describe nouns/noun phrases.
Determiners precede nouns/noun phrases and are like indicators.
The, a, an, and some are examples of determiners. For example, in the sentence the dog sleeps, the is a determiner. It precedes the noun (dog). You wouldn't say "dog sleeps" unless dog is used as a proper noun (the name of a dog, for example). You need a determiner (it doesn't have to be the, it could be "a dog sleeps").
In the sentence the brown dog sleeps, brown is an adjective. Brown describes the physical appearance of the dog (the, a, an, etc. do not). You cannot, however, simply say "brown dog sleeps." A determiner is needed (hence, the sentence is "the brown dog sleeps").
A determiner is NOT necessary when the noun is plural.
Sentences rarely start with adjectives, and adjectives do not necessarily have to precede a noun/noun phrase. (See https://www.englishgrammar.org/attributive-adjectives-nouns/ for more help with adjective placement)
Determiners cannot go after the noun/noun phrase they are associated with.
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