YOU SAID:
I am going out to eat.
INTO JAPANESE
私は外に食べに行きます。
BACK INTO ENGLISH
i'm going out to eat
INTO JAPANESE
私は食べに行きます
BACK INTO ENGLISH
i go eat
INTO JAPANESE
私は、食べに行きます
BACK INTO ENGLISH
i go eat
That didn't even make that much sense in English.