We have two cases to consider.
If 3x-7>0, then 3x-7=2.
x=3. This fits into our original requirement so this is our first solution.
If 3x-7<0, then 3x-7=-2
x=5/3. This is also valid for our original inequality, so this is our second solution.
Putting it together, x=3, 5/3