Question

(2x - 3) ^ 2 >= (x + 6)(4x - 1)

Answer 1

$(2x - 3) {}^{2} \geqslant (x + 6)(4x - 1) \\ 4 {x}^{2} - 12x + 9 \geqslant 4 {x}^{2} - x + 24x - 6 \\ 4 {x}^{2} - 12x + 9 - 4 {x}^{2} - 23x + 6 \geqslant 0 \\ - 35x + 15 \geqslant 0 \\ - 35x \geqslant - 15 \\ x \leqslant \frac{15}{35} \\ x \leqslant \frac{3}{7} \\ x \: \epsilon \: ( - \infty; \: \frac{3}{7} ]$