vs 

QUICK ANSWER
"Que le vaya bien" is a form of "que le vaya bien", a phrase which is often translated as "I hope things go well for you". "Tenga un buen día" is a phrase which is often translated as "have a nice day". Learn more about the difference between "tenga un buen día" and "que le vaya bien" below.
tenga un buen día(
tehng
-
gah
 
oon
 
bwehn
 
dee
-
ah
)
A phrase is a group of words commonly used together (e.g., once upon a time).
phrase
1.
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
(formal)
(general)
a. have a nice day
Hasta pronto, tenga un buen día.See you soon, have a nice day.
b. have a good day
Espero que mañana tenga un buen día, señorita.I hope you have a good day tomorrow, miss.
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que le vaya bien(
keh
 
leh
 
bah
-
yah
 
byehn
)
A phrase is a group of words commonly used together (e.g., once upon a time).
phrase
1.
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
(formal)
(good luck in; singular)
a. I hope things go well for you
Me alegro de que lo hayan ascendido, señor. Que le vaya bien en su nuevo puesto.I'm glad you've got promoted, sir. I hope things go well for you in your new job.
b.
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
no direct translation
Esperamos que le vaya muy bien en su entrevista.We hope your interview goes well.
Agradecermos todo su trabajo y deseamos que le vaya bien en esta nueva etapa de su vida.We thank you for all your hard work, and hope you do well in this new stage in your life.
2.
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
(formal)
(that is convenient for you; singular)
a. that suits you
Dígame un horario que le vaya bien y nos reuniremos a discutir el tema.Just tell me a time that suits you, so we can meet and discuss this issue.
3.
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
(formal)
(that is your size; singular)
a. that fits you well
Mida un pantalón que le vaya bien para saber qué talle comprar.Measure a pant that fits you well to find out what size to buy.
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