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## To find the greater integer, we can start by representing the smaller integer as x. Since the sum of the smaller and greater integers is 19, we can set up the equation x + (x+1) = 19, where x+1 represents the greater integer.

Thus, we have x + x + 1 = 19.

Simplifying, we get 2x + 1 = 19.

Next, we subtract 1 from both sides of the equation: 2x = 18.

Finally, we divide both sides by 2: x = 9.

Therefore, the greater integer is 9+1 = 10.