Thank you for the opportunity to help you with your question!
First off, congrats! You got the correct answer and you did everything correct. Only thing you are confused about is the sign change. Now, the thing with absolute value inequalities is that you need to separate them into two equations (which you did). On your second equation, "| 2x + 7 | -5 > -10", the ">" sign should have been changed to a "<" sign. This applies to all absolute value inequalities - when you are negating the second equation you have to remember to also switch the signs as well.
I hope I explained this well enough. Please let me know if you need any clarification. I'm always happy to answer your questions!