Answer :
To be able to find the length of segment AB, we'll need to find the value of the variable x;
So let's go ahead and determine what x is;
If we have a straight line drawn from point A to point C with point B being between them, then the below is true;
[tex]AB+BC=AC[/tex]Let's go ahead and substitute the given values for AB, BC and AC;
[tex]\begin{gathered} AB+BC=AC \\ 4x+6+(7x+15)=120 \end{gathered}[/tex]Solving fo x, we'll have;
[tex]\begin{gathered} 11x+21=120 \\ 11x=99 \\ \therefore x=9 \end{gathered}[/tex]Let's go ahead and find the length of segment AB;
[tex]\begin{gathered} AB=4x+6 \\ \text{But x = 9} \\ AB=4(9)+6 \\ =36+6 \\ =42 \end{gathered}[/tex]Therefore, the length of segment AB is 42.