In this problem, we are given three line segments: ik, ij, and jk. Point j lies on line segment ik. Thus, ik is broken up into two parts: ij and jk. We're also given relationships between these segment lengths.
We'll start by using the property of line segments that the sum of the lengths of two line segments that form a larger line segment is equal to the length of the larger line segment itself. This gives us the first equation:
ij + jk = ik
We're given that ij = 9, jk = x + 6, and ik = 2x. Substituting these values into the first equation, we have:
9 + (x + 6) = 2x
Solving this equation for the unknown x, we have:
15 = x
So x = 15.
Now, we substitute x = 15 into the expression for jk, which was given as jk = x + 6.
This gives us:
jk = 15 + 6 = 21
So, the numerical length of jk is 21 units.
Answer: 21 units.