The value of x in the expressions for the length measure is 4 and line segment AB has a length of 58 units.
The figure in the image is a line with a point M at the midpoint.
Since M is the midpoint of segment AB, segment AM equals segment MB.
From the figure:
Segment AM = 4x + 13
Segment MB = 3x + 17
To determine the length of segment AB, first, we find the value of x:
Since segment AM equals segment MB:
4x + 13 = 3x + 17
4x - 3x = 17 - 13
x = 4
Now, we find the length of segment AB:
Segment AB = Segment AM + Segment MB
Segment AB = 4x + 13 + 3x + 17
Segment AB = 7x + 30
Plug in x = 4:
Segment AB = 7( 4 ) + 30
Segment AB = 28 + 30
Segment AB = 58
Therefore, segment AB measures 58 units.