Songs showing up on iTunes but not iPhone 5?

I went to listen to a specific album on my iPhone 5 and noticed I only have 3 songs from it. So I went into iTunes and put the album back on to the phone. When I look at the phone through iTunes the album shows up with all the songs. However, when I look on my phone I still only have the 3 songs. They work if I create AAC versions but I don't want to do that and take up the extra space. How can I fix this?

You need to sync it. Plug the iPhone into the computer and the iPhone should say syncing.

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