How many integer values of x are there such that |x-3| + 5 < 16 ?

|x -3| < 11

With a less than, I call this a "sandwich" because the expression goes between -11 and 11

-11 <x-3 <11
add -3 to each part

-8< x <14

-8 and 14 are not included in the solution because this is less than only and doesn't include or equal.
You should be able to find the number of integers between these two integers.