Final answer:
To solve the given inequality, distribute the -2, rearrange the terms, factorize if possible, find the critical points, use test points, and create interval notation.
Step-by-step explanation:
- Distribute the -2 on the left side of the inequality: -6 + 4x < x³
- Rearrange the terms to have the polynomial on the right side: x³ - 4x - 6 > 0
- Factorize the polynomial if possible
- Find the critical points by setting the polynomial equal to 0: x³ - 4x - 6 = 0
- Use a test point from each interval to determine the sign of the polynomial
- Create an interval notation to represent the solutions of the inequality