Решите неравенство:

а) (х + 25)⋅ (х – 30) < 0;

б) (х + 6) ⋅ (х – 6) > 0;

в) (х – 1/3) ⋅ (x – 1/5) <= 0;

г) (х + 0,1) ⋅ (х + 6,3) >= 0.

Решение:

а) (х + 25)⋅ (х – 30) < 0;

(х + 25)⋅ (х – 30) = 0

x + 25 = 0 или x – 30 = 0

x = -25 x = 30

x (-25;30)

б) (х + 6) ⋅ (х – 6) > 0;

(х + 6) ⋅ (х – 6) = 0

x + 6 = 0 или x – 6 = 0

x = -6 x = 6

x (-∞; – 6) U (6;+∞)

в) (х – 1/3) ⋅ (x – 1/5) <= 0;

(х – 1/3) ⋅ (x – 1/5) = 0

x – 1/3 = 0 или x – 1/5 = 0

x = 1/3 x = 1/5

x (1/5; 1/3)

г) (х + 0,1) ⋅ (х + 6,3) >= 0.

(х + 0,1) ⋅ (х + 6,3) = 0

x + 0,1 = 0 или x + 6,3 = 0

x = -0,1 x = -6,3

x (-∞; -6,3) U (-0,1; +∞)

Источник : Учебник по Алгебре 9 класса авторов Ю.Н. Макарычев, Н.Г. Миндюк, К.И. Нешков, С.Б. Суворова, 2014г.