since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.
[tex]\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}[/tex]
