Answer:
[tex] LJ = 46 [/tex]
Step-by-step explanation:
Given:
[tex] LK = MK [/tex]
[tex] LK = 7x - 10 [/tex]
[tex] KN = x + 3 [/tex]
[tex] MN = 9x - 11 [/tex]
[tex] KJ = 28 [/tex]
Required:
LJ
Solution:
Step 1: create an equation to find the value of x
Since we are given that LK = MK, and LK = 7x - 10, let's find the expression for MK to get an equation.
[tex] MK + KN = MN [/tex] (segment addition postulate)
[tex] MK = MN - KN [/tex] (Subtract KN from each side)
[tex] MK = (9x - 11) - (x + 3) [/tex] (subtitution)
[tex] MK = 9x - 11 - x - 3 [/tex]
[tex] MK = 9x - x - 11 - 3 [/tex]
[tex] MK = 8x - 14 [/tex]
LK = MK, therefore,
[tex] 7x - 10 = 8x - 14 [/tex]
Subtract 8x from each side
[tex] 7x - 10 - 8x = 8x - 14 - 8x [/tex]
[tex] -x - 10 = -14 [/tex]
Add 10 to both sides of the equation
[tex] -x - 10 + 10 = -14 + 10 [/tex]
[tex] -x = -4 [/tex]
Divide both sides by -1
[tex] x = 4 [/tex]
Step 2: Find LJ
[tex] LJ = LK + KJ [/tex] (segment addition postulate)
[tex] LJ = (7x - 10) + (28) [/tex]
Plug in the value of x
[tex] LJ = 7(4) - 10 + 28 [/tex]
[tex] LJ = 28 - 10 + 28 [/tex]
[tex] LJ = 46 [/tex]
