ITunes will not let me transfer songs on to my iphone 4s?

Can some one help me cause the man on apple support was of no help. I downloaded music to itunes on my computer synced my iphone and it synced successfully and so i took the songs and tried to drag and drop the song to my music on my iphone it didn't work please help

Added (1). And I have songs on my iphone that aren't in my library and didn't buy them off of itunes so i just got a new computer thats why the songs aren't on there

When you connect your iPhone, it should appear on the left panel on iTunes. Click on it and you should see the info for your phone as well as the option to update and restore. At the top of this page you will see tabs. Click on the tab titled "music" and check the box where is says "sync music" then click "apply" at the lower right hand side of the screen, wait for it to finish syncing. Done.

I hear that Tipard iPhone 4S Transfer can help you transfer various files between and y you are allowed to transfer different files between any two Apple devices, and backup all your iPhone 4S SMS/MMS/Contacts as database files for further use

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