Final answer:
To find x and PQ, we can set up an equation using the fact that M is the midpoint of PQ. However, with the given values, the equation does not hold true and the correct values for x and PQ cannot be determined.
Step-by-step explanation:
To find x and PQ, we can first set up an equation using the fact that M is the midpoint of PQ. The formula for finding the midpoint of a line segment is (PQ) / 2 = PM. We can substitute the given values PM = 9x + 3 and MQ = 11x - 17 into the equation:
(9x + 3 + 11x - 17) / 2 = PQ
Simplifying the equation gives us:
20x - 14 = 2PQ
Since we are given that x = 8 and PQ = 150, we can substitute these values into the equation to find:
20(8) - 14 = 2(150)
Simplifying further:
160 - 14 = 300
146 = 300
Since this is not a true statement, it means that the given values of x = 8 and PQ = 150 are not correct.
The correct values for x and PQ cannot be determined with the information given.