Question

If k is the midpoint of JL, JK=8x+11 and KL=14x-1, find JL

Answer 1

$If\ K\ is\ the\ midpoint\ of\ JL,\ then:\\\\JK=\frac{1}{2}JL\ and\ KL=\frac{1}{2}JL\\\\therefore:\\\\8x+11=14x-1\\8x-14x=-1-11\\-6x=-12\\x=-12:(-6)\\x=2\\\\JL=2JK\Rightarrow JK=2\cdot(8\cdot2+11)=2\cdot(16+11)=2\cdot27=\boxed{54}$