〜なかった

1. 1With verbs, it states that an action did not happen in the past ('did not ~').Ex. 1
2. 2With adjectives and nouns, it states that a quality or state did not hold in the past ('was not ~').Ex. 2

It is the basic way to negate past events and states. In casual conversation and plain-style writing it is used on its own, and adding です makes it polite. For verbs, 〜ませんでした is the more standard polite form. It covers the past only, so present or future negation uses 〜ない. Besides ending a sentence, it also appears inside one, for example before ので (行かなかったので).

• 〜ないN5「〜ない」 negates present or future actions, habitual actions, and present states; 「〜なかった」 is its past form and negates only the past. They share the same conjugation pattern but differ in tense, so they cannot be swapped.
• 〜は〜ではありませんN5「〜は〜ではありません」 is a polite, present-tense negative judgment that attaches only to nouns and な-adjectives; 「〜なかった」 is the plain past negative and can attach to verbs, adjectives, and nouns. They differ in both tense and register, so they cannot be swapped.
• たことがあるN5「〜なかった」 denies a specific fact at a past time (e.g., didn't go yesterday); 「たことがある」 is about whether one has ever had an experience, and its negative 「たことがない」 means 'have never done...' and is not used for specific events like yesterday. They cannot be swapped.
• ずにN3「ずに」 attaches only to verbs and links clauses within a sentence, meaning 'without doing...' or '... instead of ...', and leans written/formal; 「〜なかった」 is a predicate form of past negation that can also attach to adjectives and nouns. They cannot be swapped.
• なくてもいいN4「なかった」 states the fact that something was not done or was not the case in the past; 「なくてもいい」 means it's okay not to do something or for something not to be the case, expressing exemption from obligation or permission, and does not indicate the past. Both derive from the ない-form, but they cannot be swapped.
• ということだN3「〜なかった」 is a conjugated form that negates past actions or states; 「ということだ」 attaches to plain forms and means 'I heard that...' or 'in other words...', carrying no negative meaning itself. They cannot be swapped, but they can be combined: 「来なかったということだ」.

〜ない is the non-past negative ('don't / won't'), and 〜は〜ではありません is the polite non-past noun negative (its past is ではありませんでした), whereas 〜なかった places the negation in the past. Unlike たことがある (experience), ずに ('without doing', a connective leading into another clause), なくてもいい ('don't have to'), and ということだ (hearsay or meaning), 〜なかった is simply the plain past negative form stating that something did not happen or was not so, whether it ends the sentence or continues it (行かなかったので).