To solve the open sentence 2x + y < 6, we need to find the values of x and y that make the inequality true, given that x and y are positive integers. One way to approach this is to use trial and error. We can start by plugging in the smallest possible values for x and y, which are both 1, and see if the inequality holds: 2(1) + 1 < 6, which is true. We can try other values of x and y that satisfy the condition that they are positive integers, such as x = 1, y = 2, x = 2, y = 1, and x = 2, y = 2. We find that only the first case, x = 1 and y = 2, satisfies the inequality. Therefore, the solution to the open sentence 2x + y < 6, where x and y are positive integers, is (x, y) = (1, 2).