Final answer:
To solve the inequality involving a quadratic and a rational expression, one should apply algebraic methods such as completing the square or using the quadratic formula, and then verify the solutions against the original inequalities' conditions.
Step-by-step explanation:
When solving the inequality 15 ÷ (2 - 3x) ≥ x² - 2, we must be careful with possible mathematical operations like completing the square, applying the quadratic formula, and checking the ranges of possible solutions for x. If we simplify the given inequality or a similar quadratic equation, we would likely need to identify the values of a, b, and c to use in the quadratic formula, which is −b ± √(b² - 4ac) / (2a). After finding the roots of the quadratic equation, we must check these solutions back in the original inequality to ensure they don't produce any undefined conditions, such as division by zero, and to verify which portions of the solution set satisfy the inequality.