If J is between H and K then HJ + JK = HK.
We have:
HJ = x - 5, JK = 5x - 12 and HK = 37.
The equation:
(x - 5) + (5x - 12) = 37
(x + 5x) + (-5 -12) = 37
6x - 17 = 37 |+17
6x = 54 |:6
x = 9
HJ = x - 5 → HJ = 9 - 5 = 4
JK = 5x - 12 → JK = 5(9) - 12 = 45 - 12 = 33
Check:
HJ + JK = KH
4 + 33 = 37 CORRECT :)
