Answer:
LJ = 46
Step-by-step explanation:
Given information:
- LK = MK
- LK = 7x - 10 ⇒ MK = 7x - 10
- KN = x + 3
- MN = 9x - 11
- KJ = 28
Segment Addition Postulate
If point B lies on the line segment AC, then AB + BC = AC.
Apply the Segment Addition Postulate to MN to find the value of x:
⇒ MN = MK + KN
⇒ 9x - 11 = 7x - 10 + x + 3
⇒ 9x - 11 = 7x + x - 10 + 3
⇒ 9x - 11 = 8x - 7
⇒ 9x - 11 - 8x = 8x - 7 - 8x
⇒ x - 11 = -7
⇒ x - 11 + 11 = -7 + 11
⇒ x = 4
Now we have found the value of x, we can calculate LJ, again applying the Segment Addition Postulate:
⇒ LJ = LK + KJ
⇒ LJ = 7x - 10 + 28
Substitute the found value of x into the equation:
⇒ LJ = 7(4) - 10 + 28
⇒ LJ = 28 - 10 + 28
⇒ LJ = 18 + 28
⇒ LJ = 46
