It is incorrect because "alternate" has nothing to do with "alternatives" at all.
Alternate has to do with a repeating pattern and the action of changing between segments of a pattern.
(It is a verb)
Alternative indicates there are two or more options from which to choose one option...it is a noun.
So they sound similar but are actually 2 completely different words and are not interchangeable.
Incorrect? Yes. But, it was a road sign, so you have a matter of seconds to read it. When reading that very quickly (as you would when driving), it could easily be confused by some as being read as 'find alternative route', which is easy to understand. Or, the sign may not have been big enough for 2 extra letters??
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