SOLUTION: The sum of two consecutive integers does not exceed 19. Find the range of values of the larger integer?

Let the larger be x, then the smaller is 1 less, or x-1

So x + (x-1) ≤ 19
   x + x - 1 ≤ 19
      2x - 1 ≤ 19
          2x ≤ 20
           x ≤ 10

The larger integer must be less than or equal 10.

It wasn't mentioned in the problem, but if the integers 
must be positive then the larger would also have to be 
greater than or equal to 2, so that the smaller would be 
1 or more.

Edwin