Final answer:
To solve the inequality 2x^3 - 3x^2 ≥ 14x, rearrange the terms to form a quadratic equation and factor it. The solution is x ≥ 2.
Step-by-step explanation:
To solve the inequality 2x^3 - 3x^2 ≥ 14x, we need to rearrange the terms to form a quadratic equation.
- Subtract 14x from both sides of the inequality: 2x^3 - 3x^2 - 14x ≥ 0.
- Factor out the common term x: x(2x^2 - 3x - 14) ≥ 0.
- Factor the quadratic equation: (x - 2)(2x + 7)(x + 1) ≥ 0.
- Determine the intervals where the expression is greater than or equal to zero: x ≥ -1 and x ≥ 2.
The solution to the inequality is x ≥ 2.