School help needed!

[Yabba]

If anyone can help me with this equation it would be much apreciated

5+|3x+2|=|x-7|

I know I sound like the hundreds of lazy students who do not want to do math homework, but this type of absolute value equation is explained no where in the text book. This problem was our only homework but "experienced" math teacher did not explain how to do it. I just want an explanation on how to do this type of equation, I do not care if you just post and solve an example, I just need an explanation.

 

[Pinkamena]

This picture should get you started. You need to find "when", i.e. for what x-values the two functions have the same y-values (the places where they cross each other). Those two x-values are then your answers.