largely
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largely
For the most part, almost completely, or as far as possible. It expresses that something applies to a very high degree, but small exceptions are possible.
Nach der Renovierung sind die Mängel am Gebäude weitestgehend behoben.
After the renovation, the defects in the building have largely been fixed.
The word is made up of the superlative of 'weit' (far) as 'weitest-' and the participle 'gehend' (going). The literal meaning is 'going the farthest', which explains the figurative meaning 'to the greatest possible extent'.
Die beiden Parteien haben eine weitestgehende Einigung erzielt.
The two parties reached a far-reaching agreement.
As an adverb, 'weitestgehend' (largely) usually appears in the middle of the sentence (in the Mittelfeld). It often modifies a verb, a participle, or an adjective that follows it.
Die Software ist mit allen gängigen Betriebssystemen weitestgehend kompatibel.
The software is largely compatible with all common operating systems.
'Weitestgehend' (largely) belongs more to formal written language and is often used in reports, official communications, or business contexts. It sounds more elevated and precise.
Die Forderungen der Mitarbeiter wurden vom Unternehmen weitestgehend erfüllt.
The employees' demands were largely met by the company.
almost
'fast' and 'weitestgehend' both say that something is not quite complete. 'fast' is very general and fits many everyday situations when only a small part is missing. 'weitestgehend' sounds somewhat more formal and emphasizes that something is largely done, clarified, or achieved. It fits especially well with plans, rules, work, or reports. Put simply: 'fast' is neutral and short, while 'weitestgehend' sounds more precise and often more factual.
Die Vorbereitungen für die Reise sind weitestgehend abgeschlossen.
The preparations for the trip are largely complete.
Die Küche ist fast sauber, nur der Tisch muss noch abgewischt werden.
The kitchen is almost clean; only the table still needs to be wiped down.