Final answer:
The value of x is determined to be 7.2 by setting up the equation 25 - x + 8 = 19x - 111 based on the distances between points P, Q, and R and solving for x.
Step-by-step explanation:
The question asks to find the value of x when given that point Q is between points P and R, with distances PO=25, OR=-x+8, and PR=19x-111. To solve for x, we consider that the sum of PO and OR should be equal to PR since Q is between P and R on a line segment. Therefore, the equation is PO + OR = PR. Substituting the given values, we have 25 + (-x + 8) = 19x - 111.
By simplifying and solving the equation, you get:
25 - x + 8 = 19x - 111
33 - x = 19x - 111
Adding x to both sides and adding 111 to both sides gives:
33 + 111 = 19x + x
144 = 20x
Dividing both sides by 20 gives:
x = 144 / 20
x = 7.2
Therefore, the value of x is 7.2.