HJ=25
JK=25
HK=50
Explanation
Step 1
J is the midpoint, it means
[tex]HJ=JK[/tex]
Step 2
replace andsolve for x
[tex]\begin{gathered} HJ=JK \\ 9x-2=4x+13 \\ \text{subtract 4x in both sides} \\ 9x-2-4x=4x+13-4x \\ 5x-2=13 \\ add\text{ 2 in both sides} \\ 5x-2+2=13+2 \\ 5x=15 \\ divide\text{ both sides by 5} \\ \frac{5x}{5}=\frac{15}{5} \\ x=3 \\ \end{gathered}[/tex]
Step 3
finally replace the valure of X to find HJ and JK
[tex]\begin{gathered} HJ=JK=9x-2=9\cdot3-2=27-2=25 \\ HJ=25 \\ JK=25 \\ then \\ HK=HJ+JK=25+25 \\ \\ HK=50 \end{gathered}[/tex]
I hope this helps you
