Nobu gave you the meaning of the last sentence but watch out, it's not おくわけ, it's ておく+わけにもいかない (sometimes written as わけにはいかない). ておく roughly means "doing something in advance, in preparation for the future" while わけにも行かない means "cannot do something". You'll meet it on any jlpt n2 book. Dunno if this was of any help to you but hopefully breaking down those two grammar forms will give you a better understanding of the structure of this sentence and its meaning as a whole :)
You're welcome theamoo! If you're studying for the n3 there's time for わけにもいかない. Anyway, there's nothing wrong with writing 置く when you mean to say "to put/place", but when you've to use ておく as "to do something in advance" then おく becomes an auxiliary verb so leave it as it is in its kana form. To help you understand why take a look at the following example: 会議中はスマホを裏返して置いておく。Do you see now how grammatically different are て置く（て置いて）and ておく? They play different roles, that's why you have to be careful not to confuse them. One more thing, keep in mind that ておく when placed after causative verbs, the ones with させる, can assume the meaning of "leave/allow somebody do something". To make it simpler: 昼寝（を）する to take a nap --> 昼寝させる to lay someone down for a nap/get someone to nap/put down to sleep (gosh this sounds threatening hehe) --> 昼寝させておく to leave someone sleep. Ok? I tried to keep it as short and simple as possible, hope it helps! :)
Ah I see! You're right they are very different. Thank you so much for the great explanation! Do you mind if I ask what books or study guides you've used for grammar? You have a great understanding of the grammar 😊
Yep :) The first ておいて（て置いて） stands for "to put/place" while the last one holds an auxiliary form. Let's just break it down like this: Xを裏返して置い[ておいてください] --> "X on the other way put[and leave it as it is/do it in view of the meeting]", but of course if you had to translate that sentence you'd simply say "lay your smartphone face down".
As for the grammar books I've used, here are the titles I've put my hands on along my studies 新文化初級日本語1 - actually this is a textbook but it had some good grammar explanations here and there... my very first Japanese book Do it yourself - Japanese grammar review (although it's aimed at beginners, it goes on explaining some keigo and some N3 grammar rules) 日本語チャレンジ just like "do it yourself" but way better, very informative An integrated approach to intermediate Japanese grammar TRY 日本語能力試験 (for N3/N2) 日本語能力試験問題集(for N3/N2)文法スピードマスター for some reason I liked this better but TRY was very helpful nonetheless 日本語総まとめ(for N3/N2) 新完全マスター(only for N2) all the three tomes of "A Dictionary of Japanese Grammar"; contrary to the other books ADJG's got plenty of explanations, but each one of the books I've listed mentionsome piece of information left out by their counterparts. I don't know which one you already have, but if you are interested some of these books are available online on pdf, just google them. ;)