\(\left\{\begin{array}{ccc}a&for& a\geq0\\-a&for&a \ \textless \ 0\end{array}\right \\\\3|x-3|+2=14\ \ \ |subtract\ 2\ from\ both\ sides\\\\3|x-3|=12\ \ \ \ |divide\ both\ sides\ by\ 3\\\\|x-3|=4\iff x-3=4\ or\ x-3=-4\ \ \ |add\ 3\ to\ both\ sides\\\\\boxed{x=7\ or\ x=-1}\)
