Final answer:
In this geometry problem, the value of x is found to be 6 by applying the Segment Addition Postulate and algebraic manipulation to the given segment lengths. The lengths of segments JK and KL are then determined to be 12 and 8, respectively.
Step-by-step explanation:
The student is working with a segment addition problem in geometry. Given three points J, K, and L in a line segment, with K being between J and L, we have the segment lengths JK, KL, and JL.
The equation relevant to the segment lengths given is:
JK = 2x
KL = x + 2
JL = 5x - 10
By the Segment Addition Postulate, we know that JK + KL = JL. Therefore, when we combine the equations above, we get: (2x) + (x + 2) = (5x - 10).
Combining like terms gives us 3x + 2 = 5x - 10. Solving for x requires subtracting 3x from both sides, yielding 2 = 2x - 10, and then adding 10 to both sides, resulting in 12 = 2x. So, x equals 6.
When we substitute x back into the equations for JK and KL, we find that JK = 2(6) = 12, and KL = 6 + 2 = 8.
Therefore, the value of x is 6, JK is 12, and KL is 8.