Question

Point M is the midpoint of segment JK. Find JK when JM=6x-7 and MK=2x+3.

Answer 1

6x-7 = 2x+3

 add 7 to each side

= 6x = 2x+10

 subtract 2x from each side

4x=10

divide both sides by 4

 x = 10/4 = 5/2

6(5/2)-7 = 8

8*2 = 16

 JK is 16

Answer 2

If M is the midpoint of JK then JM+MK=JK and JM=MK
so
6x-7=2x+3
minus 2x both sides
4x-7=3
add 7 both sides
4x=10
divide both sides by 4
$x=\frac{10}{4}$
$x=\frac{5}{2}$

sub back

JM=6x-7
$JM=6(\frac{5}{2})-7$
$JM=\frac{30}{2}-7$
$JM=15-7$
JM=8

JM=MK=8
JM+MK=8+8=16=JK

$x=\frac{5}{2}$ and JM=8=MK and JK=16