Question

Suppose JM= 5x-10 and MK= x+14 and M is the midpoint of JK. Find x and JM

Answer 1

Because M is the midpoint of segment JK, JM=MK.

Now, substitute, and you will get 5x-10=x+14.
You can easily solve from here.


5x-10=x+14
5x-x-10=x-x+14
4x-10=14
4x-10+10=14+10
4x=24
4x/4=24/4
x=6

Since we now know x=6 and the two segments are congruent, both JM and MK are 6.

JM+MK= 6+6=12, therefore JK=12.