If M is the midpoint of segment AB, and #AM = 3x + 5# and #BM = 4x – 10#, what is the length of AB?

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Answer 1 · 2016-09-10T14:35:36

#AB = 100#

The fact that M is the midpoint means that the distance from M to the two endpoints, A and B is the same.

We have: #BM = AM#

#4x-10 = 3x+5#

#4x-3x = 5+10#

#x = 15#

#AM= 3x+5 = 3(15)+5#

#AM = 50#

Check: #BM = 4x-10 = 4(15)-10#

#BM = 50#

#AB = AM + BM#

#AB = 50+50#

#AB = 100#