Решите уравнение: 1) |x| + 3x = 12; 2) |x| − 4x = 9; 3) 2(x − 5) − 6|x| = −18.

Решение 1

|x| + 3x = 12 x > 0: x + 3x = 12 4x = 12 x = 12 : 4 x = 3; x < 0: −x + 3x = 12 2x = 12 x = 12 : 2 x = 6.

Решение 2

|x| − 4x = 9 x > 0: x − 4x = 9 −3x = 9 x = 9 : −3 x = −3 x < 0: −x − 4x = 9 −5x = 9

Решение 3

2(x − 5) − 6|x| = −18 x > 0: 2x − 10 − 6x = −18 2x − 6x = −18 + 10 −4x = −8 x = −8 : −4 x = 2 x < 0: 2x − 10 + 6x = −18 2x + 6x = −18 + 10 8x = −8 x = −8 : 8 x = −1