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Record player attached to an amplifier revising IB physics

I have some problems about Operational Amplifiers from the communication option. I have had three mental breakdowns in class now.. Why do we need an inverting and a non-inverting amplifier. Its name suggest the concept of amplifying signals, then WHY would we want an inverting one? I mean, it doesn't help by inverting the signal sent. It's like playing a song backwards. It just doesn't make sense!
I know all the theory of drawing it and calculating gain and stuff, but why do we have them?
What use do they have?
- Camilla