Verified answer

2)

[tex]11 - {(x + 1)}^{2} \leqslant x \\ 11 - {x }^{2} - 2x - 1 \leqslant x \\ {x}^{2} + 3x - 10 \geqslant 0 \\ x1 = 2 \\ x2 = - 5 \\ (x - 2)(x + 5) \geqslant 0[/tex]

(-∞;-5]&[2;+∞)

4)

[tex]5x(x + 4) - (2x - 3)(2x + 3) > 30 \\ 5 {x}^{2} + 20x - 4 {x}^{2} + 9 - 30 > 0 \\ {x}^{2} + 20x - 21 > 0 \\ x1 = - 21 \\ x2 = 1 \\ (x + 21)(x - 1) > 0[/tex]

(-∞;-21)&(1;+∞)

5)

[tex](3x - 7)(x + 2) - (x - 4)(x + 5) > 30 \\ (3 {x}^{2} - x - 14) - ( {x}^{2} + x - 20) - 30 > 0 \\ 2 {x}^{2} - 2x - 24 > 0 \\ {x}^{2} - x - 12 > 0 \\ x1 = - 3 \\ x2 = 4 \\ (x + 3)(x - 4) > 0[/tex]

(-∞-3)&(4;+∞)