Final answer:
To find the value of x, the lengths of the segments AB, BC, and AC are used. Since AC is the total length, AB + BC should equal to AC. By setting up the equation (8x + 7) + 18 = 65 and solving for x, we find that x equals 5.
Step-by-step explanation:
The question provides the lengths of segments AB, BC, and AC where point B is between points A and C. We know that AB is equal to 8x + 7, BC is equal to 18, and AC is the total length which is given as 65. To find the value of x, we can use the concept that the total length AC is equal to the sum of lengths AB and BC. Therefore, we can set up the equation:
AB + BC = AC
(8x + 7) + 18 = 65
To solve for x, we first simplify the equation by adding the constant terms:
8x + 25 = 65
Next, we subtract 25 from both sides to isolate the term with x:
8x = 40
Lastly, we divide both sides by 8 to find the value of x:
x = 5
Thus, the value of x is 5, which corresponds to option (b).