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Given that −7 < x < 18 and 9 < y < 20, what is the interval of possible values of x + y?

1. [2, 38]
2. (2, 38)
3. [2, 38)
4. (2, 38]

Correct answer: (2, 38)

Solution

The minimum value of x + y occurs when x is at its lowest (-7) and y at its lowest (9), resulting in -7 + 9 = 2. The maximum occurs when x is at its highest (18) and y at its highest (20), giving 18 + 20 = 38. Since x and y do not include their endpoints, the sum x + y will also not include 2 and 38, leading to the interval (2, 38).

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