I've learned that both "lejos" and "alejados" mean "far" / "far away".
What are the differences between these words? When should you prefer one over the other?
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"lejos" is an invariable adverb.
"alejado" is an adjective whose gender and number varies according to the noun to which it refers.
Both tend to appear within the predicate, after verbs like "estar", "encontrarse" or "quedar", but "lejos" is much more usual and "alejado/a/s" can sound a little more formal or literary. Also note that the verb "quedar" is only used for things.
Both "lejos" and "alejado/a/s" can also be used attributively (after, never before the noun they refer to) but will always tend to be followed by a prepositional phrase with "de":
Vive en una casa lejos del centro. (He/She lives in a house far from downtown.)
Vive en una casa alejada del centro. (He/She lives in a house far from downtown.)
There is an important difference between "lejos" and "alejado/a/s" and that is that "lejos" can refer to a temporary/occasional or permanent distance, while "alejado/a/s" almost always refers to a permanent distance and will thus tend to be used for properties or locations being far from other places.
(Nosotros) Estamos / Nos encontramos lejos del centro (we are far from downtown). (temporary or permanent distance)
Nuestra casa está / se encuentra / queda lejos del centro (our house is far from downtown). (permanent distance)
Nuestra casa está / se encuentra / queda alejada del centro (our hourse if far from downtown). (permanent distance)
I recommend that you use "lejos" at all times: it's invariable and will always sound right.
Note: "estar alejado" (NOT "estar lejos") can be used for a temporary, emotional rather than physical distance, though in this case I prefer "estar distanciado", e.g. Estoy alejado / distanciado de mi familia (I am estranged from my family).
La casa queda lejos de la playa. The house is far (away) from the beach.
La casa [en le terreno] está alejada de la calle. The house is located away from the street. Or: The house is at a distance from the street. Or: The house is away from the street. Or: The house is not close to the street. Or: The house is far away from the street.
Be careful: In English, in everyday language both **alejada and lejos can be translated the same way in certain contexts.**
Quiero alejarme de ti. I want to get away from you or distance myself from you.
Quiere irme lejos de ti. I want to go far away from you.
alejarse is a verb and implies moving a distance away from a person or thing or being at a distance away from something or distancing oneself from something.
lejos is just the adverb for far away from.
In English, the only verb for alejarse de alguien" is **to distance oneself from someone. Otherwise, one has to use: go far away from or get away from.
I'm contributing another answer because I sense that OP was hoping for a simple explanation without a lot of jargon.
"Lejos" is an adverb and would be a common choice to describe the location of something, for example
"Alejado" is an adjective, and is often used for emotional distance, for example
It is also possible, but less common, to use "alejado" to mean "far" or "far away" in the sense of "remote," for example:
As an adjective, "alejado" will need to agree with the noun it describes, in number and gender. Here's an example with a feminine noun:
(For a more complete listing of sample sentences and possible usages, I would encourage you to check some dictionaries.)