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First time poster, puzzle is rather short:

AEIOLN = KAOLINE

OLT = JOLT

AEILNTR = ???

Edit: One more example to help guide your way to my hoped for pattern (answers from before this may break, but are all very good).

CJK = JACK, JOCK

Edit 2: Another example (last one, think about word games):

AIFR = FAQIR

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We have established by now that the answer is ...

... an anagram of the given letters plus one additional letter. According to the OP, not all such answers are valid, though.

There is a hint in the title:

"Scrambbled" is "scrambled" plus the letter "b", but it might also be "scrabbled" plus "m".

Let's follow this hint and ...

... determine the Scrabble scores for the example answers:

KAOLINE: 11
JOLT: 11
JACK: 17
JOCK: 17
FAQIR: 17

These scores are not the same for all answers, but they share a common property: They are all prime numbers.

The answer is therefore:

INTERVAL with a Scrabble score of 11. (There's also "inflater" with the same score, but "interval" seems to be a more common word.)

Thanks, feelinferrety, for doing the legwork of finding the possible anagrams.

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AEIOLN = KAOLINE

OLT = JOLT

AEILNTR = ???

INERTIAL
There are many possibilities that can be made from adding a letter and unscrambling, but since you added 'k' in the first instance, then 'j', the next one you add 'i' and the only possibility is inertial.

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  • $\begingroup$ Not quite what I was going for (how did I only pick JOLT and KAOLINE for the other two?) $\endgroup$ – Adam Martin Jun 9 '16 at 2:48
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    $\begingroup$ @AdamMartin Edited to show a pattern. $\endgroup$ – Inazuma Jun 9 '16 at 2:52
  • $\begingroup$ Not the pattern I was looking for but +1! $\endgroup$ – Adam Martin Jun 9 '16 at 2:53
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AEILNTR

Since we are given only two solved cases, I can only speculate as to the actual rules and intended answer, so I'll list my own process of elimination below to offer a solution.

RULE 1

Anagrams made possible with the addition of one extra letter:

Result:

C : clarinet
E : entailer
F : inflater
G : triangle tanglier relating integral altering alerting
I : inertial
M : tramline terminal
N : internal
O : relation oriental
P : triplane
S : retinals ratlines latrines entrails
V : interval

RULE 2

Anagram contains the vowels listed in the order listed. FAILED
The anagram begins with the additional letter.

Result:

clarinet, entailer, inertial, oriental

RULE 3

The additional letter does not repeat an existing letter.

Result:

clarinet, oriental

RULE 4

The additional letter is a consonant.
Bonus: Result is a noun.

Result and ANSWER:

CLARINET

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  • $\begingroup$ Nice thought process, but I'm going to add a little tidbit in the question to hint at my aimed pattern which no one has gotten yet which will break some of these (just FYI). +1 $\endgroup$ – Adam Martin Jun 10 '16 at 23:30
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AEIOLN = KAOLINE

OLT = JOLT

AEILNTR = ???

IALNITER

First letter might be in sequence 'k' in the first, then 'j', so the next one can be 'I'.

Then you have selected the first letter from the 2 words. 'A' in first and 'o' in the second.

Then you have gone to middle letter and then from left to right the letters are interchanged.

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Clarinet, Interval... There are many words. Do you want them all?

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  • $\begingroup$ Nope, there are more words for the first two examples that aren't listed. $\endgroup$ – Adam Martin Jun 12 '16 at 23:49

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