Question

Найдите целые решения неравенства
(2x + 3)(x + 1) ≤ x² + 9.

Answer 1

(2x + 3)(x + 1) ≤ x^2 + 9

x^2 + 2x + 3x + 3 ≤ x^2 + 9

x^2 + 5x + 3 ≤ x^2 + 9

x^2 + 5x + 3 - x^2 + 9 ≤ 0

x^2 + 6x - x - 6 ≤ 0

x(x + 6) - (x + 6) ≤ 0

(x + 6)(x - 1) ≤ 0

x + 6 ≤ 0 ; x - 1 ≥ 0

x + 6 ≥ 0 ; x - 1 ≤ 0

x∈[ - 6 ; 1]