How many integer side lengths are possible to complete a triangle in which the other sides measure 6 units and 3 units?
To solve this problem, I need to recall the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. This means that I have to find all the integer values of x such that 6 + 3 > x, 6 + x > 3, and 3 + x > 6. The first inequality, 6 + 3 > x, implies that x < 9. The second inequality, 6 + x > 3, implies that x > -3. The third inequality, 3 + x > 6, implies that x > 3. Combining these three inequalities, I get that 3 < x < 9. The only integer values that satisfy this condition are 4, 5, 6, 7, and 8. Therefore, there are 5 possible integer side lengths for the third side of the triangle. 