Question

What are the steps for solving the given inequality for x: -2(3-2x) < x³?

Answer 1

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:

1. Distribute the -2 on the left side of the inequality: -6 + 4x < x³
2. Rearrange the terms to have the polynomial on the right side: x³ - 4x - 6 > 0
3. Factorize the polynomial if possible
4. Find the critical points by setting the polynomial equal to 0: x³ - 4x - 6 = 0
5. Use a test point from each interval to determine the sign of the polynomial
6. Create an interval notation to represent the solutions of the inequality