Final answer:
To find x and QS, use the given information about line segment lengths. Set the lengths equal to each other, solve for x, then substitute the value of x to find QS.
Step-by-step explanation:
To find x and QS, we can use the given information about the lengths of the line segments. We are given that PQ = QR and PQ = x + 5 and QR = 3x - 5. Setting these equations equal to each other, we have x + 5 = 3x - 5. Solving this equation will give us the value of x. Then, we can find QS by substituting the value of x back into the equation QS = PS - PQ.