Answer:
JL = 21
Step-by-step explanation:
Given that K is on line segment JL, therefore:
KL + JK = JL (according to segment addition postulate)
KL = 2x - 2
JK = 5x + 2
JL = 4x + 9
Thus:
[tex] (2x - 2) + (5x + 2) = (4x + 9) [/tex]
Solve for x
[tex] 2x - 2 + 5x + 2 = 4x + 9 [/tex]
[tex] 2x +5x - 2 + 2 = 4x + 9 [/tex]
[tex] 7x = 4x + 9 [/tex]
Subtract 4x from both sides
[tex] 7x - 4x = 4x + 9 - 4x [/tex]
[tex] 3x = 9 [/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{9}{3} [/tex]
[tex] x = 3 [/tex]
Find the numerical length of JL
[tex] JL = 4x + 9 [/tex]
Plug in the value of x
[tex] JL = 4(3) + 9 = 12 + 9 = 21 [/tex]
