Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 14, and 19, what is the value of r?	Choose one:
A) 20	B) 21	C) 26	D) 27	E) 33
From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are:   1. q + 14 &gt; 19   2. 14 + 19 &gt; q   3. q + 19 &gt; 14   Equation 3 is true for any positive value of q.   From equation 1, q &gt; 5   From equation 2, 33 &gt; q   Then 33 &gt; q &gt; 5 so q can be any value from 6 to 32 inclusive.   The number of possible values is 27.   The answer is 27.
<result>D</result>
Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 14, and 19, what is the value of r?