Final answer:
The value of variable x in the line segments problem is 5. By adding the lengths of segments AB and BC, setting the sum equal to segment AC, and solving for x, we find the necessary value.
Step-by-step explanation:
The student's question involves solving for a variable within a geometric scenario using the properties of line segments. Given that Segment AB = 2x - 3, Segment BC = 9, and Segment AC is the entire length and equals 16, we can derive an equation to find the value of x. This is based on the property that the sum of the lengths of segments AB and BC should equal the length of AC, when the points A, B, and C lie on a straight line.
To solve for x, we set up the equation AB + BC = AC, which gives us (2x - 3) + 9 = 16. Simplifying this, we get 2x + 6 = 16. Subtract 6 from both sides to obtain 2x = 10, and dividing both sides by 2 yields x = 5.