x(4x + 1) - 7(x^2 - 2x) < 3x(8 - x)

1. Expand both sides: 4x^2 + x - 7x^2 + 14x < 24x - 3x^2.
2. Combine like terms: -3x^2 + 15x < 24x - 3x^2.
3. Add 3x^2 to both sides: 15x < 24x.
4. Subtract 15x from both sides: 0 < 9x.
5. Divide by 9: 0 < x, or x > 0.