2|x - 5| + 2 = 12
        
Subtract 2 from both sides

              2|x - 5| = 10

Divide both sides by 2

               |x - 5| = 5

That would be true whether x - 5 = 5 or whether it equals -5.
So we take both cases:

      x - 5 = 5           x - 5 = -5
          x = 10              x = 0

Smaller solution = 0, Larger solution = 10

Edwin