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"La solidaridad" is a form of "solidaridad", a noun which is often translated as "solidarity". "El favor" is a form of "favor", a noun which is often translated as "favor". Learn more about the difference between "la solidaridad" and "el favor" below.
la solidaridad(
soh
-
lee
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dah
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ree
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dahd
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (general)
a. solidarity 
El nuevo alcalde rechazó el aumento salarial para mostrar solidaridad con los empleados del ayuntamiento.The new mayor rejected his salary increase to show solidarity with the city hall employees.
b. support 
El equipo donó un millón de euros en solidaridad con los refugiados.The team donated a million euros in support of the refugees.
el favor(
fah
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bohr
)A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).
1. (help)
a. favor  (United States)
Regionalism used in the United States
Si quieres que alguien te haga un favor, solo tienes que saber pedírselo.If you want a favor from someone, you just need to know how to ask for it.
b. favour  (United Kingdom)
Regionalism used in the United Kingdom
¡No te olvides de darle las gracias por ofrecerse a hacerte el favor!Don't forget to thank him for offering to do you a favour!
2. (support)
a. favor  (United States)
Regionalism used in the United States
Trató de cambiar su personalidad para ganarse el favor de los votantes.He tried to change who he was in order to gain the favor of the voters.
b. favour  (United Kingdom)
Regionalism used in the United Kingdom
Esto le hizo perder el favor de los comunes.This made him lose the favour of the Commons.