Learn Turkish: İnsanlar çamaşırları makine ile yıkamıyordu çünkü elektrik yoktu. - People used not to wash laundry with a machine because there was no electricity.

It starts with the verb root yıka- (to wash). To make it negative before the -yor suffix, we would normally use -ma-, but the -yor suffix "narrows" an a or e before it into ı, i, u, or ü. So the negative part becomes -mı-. Finally, we add -du for the past tense. This gives us yıka + mı + yor + du.

Usually -yordu means "was doing". Why is it translated as "used not to wash" here?

The Turkish past continuous tense (-yordu) has two main uses: actions that were happening at a specific moment in the past ("was washing"), and ongoing past habits ("used to wash"). Because the sentence talks about a general era before electricity (çünkü elektrik yoktu), it is describing a past habit, so "used not to wash" makes the most sense in English.

Since the subject is İnsanlar (people, plural), shouldn't the verb be plural like yıkamıyorlardı?

In Turkish, if you already state a plural subject (especially humans, like İnsanlar), you don't have to add the plural suffix (-lar) to the verb. Saying yıkamıyorlardı would also be correct, but leaving it singular as yıkamıyordu is very common and completely natural.