1. The problem asks for the range of possible sizes for side $x$ of a triangle with the other two sides being 8.5 and 8.0. 2. According to the triangle inequality theorem, for any triangle with sides $a$, $b$, and $c$, the length of any side must be less than the sum of the other two sides and greater than the absolute difference of the other two sides. 3. Applying this to side $x$, we have: $$|8.5 - 8.0| < x < 8.5 + 8.0$$ 4. Calculate the values: $$|0.5| < x < 16.5$$ 5. Therefore, the range of possible sizes for side $x$ is: $$0.5 < x < 16.5$$ This means $x$ must be greater than 0.5 and less than 16.5 to form a valid triangle.