Answer
JK is 42.
KL is 78.
Work Step by Step
$\overline{JK}+\overline{KL}=\overline{JL}\longrightarrow$ Segment Addition Postulate
$(4x+6)+(7x+15)=120\longrightarrow$ Substitute
$11x+21=120\longrightarrow$ Combine like terms
$11x+21-21=120-21$ Subtract 21 from each side
$11x=99\longrightarrow$ Simplify
$11x\div11=99\div11\longrightarrow$ Divide each side by 11
$x=9$
Substitute to find the lengths of each segment.
JK is $4x+6=4(9)+6=36+6=42$
KL is $7x+15=7(9)+15=63+15=78$
