It should be compatible, but the HP Pavilion DV7-3188cl uses an Intel HM55 chipset which will only support SATA2 (3Gbps) speeds.
To get the best speeds possible, you will have to select the 'high performance' power profile from Windows 7. You will however be restricted to speeds of around 260 MB/s max.
If the laptop has an HDD, then you'll find a massive boost to performance once you fit the SSD. IF there is already an SSD in the laptop, then you probably won't find a huge difference in performance over the existing SSD.
Buy the 'laptop kit' version of the 840 EVO, is it's supplied with a USB to SATA converter, and software to allow you to easily migrate your existing Windows 7 installation over to the SSD.