Graph of a cubic polynomial illustrating the solution to a polynomial inequality, with key points labeled on the x-axis.

Graph showing a cubic polynomial function y = P(x) with a curve intersecting horizontal lines y = 1 and y = 2, indicating the solution set for the inequality 1 < x³ - (1/2)x² - (7/2)x + 2 ≤ 2. The x-values where the curve intersects these lines are labeled a, b, c, d, e, f.