Tentukan himpunan penyelesaian dari pertidaksamaan berikut

Jawaban:

1. |4x + 9| ≥ |x + 6|

= |4x + 9|² ≥ |x + 6|²

= (4x + 9)² ≥ (x + 6)²

= (4x + 9)² – (x + 6)² ≥ 0

= (4x + 9 + x + 6) (4x + 9 – (x + 6)) ≥ 0

= (5x + 15) (4x + 9 – x – 6) ≥ 0

= (5x + 15) (3x + 3) ≥ 0

= 5x + 15 = 0 atau 3x + 3 = 0

5x = -15 3x = -3

x = -3 x = -1

HP {–3,–1}

2. |6x – 3| ≥ |4x + 13|

= |6x – 3|² ≥ |4x + 13|²

= (6x – 3)² ≥ (4x + 13)²

= (6x – 3)² – (4x + 13)² ≥ 0

= (6x – 3 + 4x + 13) (6x – 3 – (4x + 13)) ≥ 0

= (10x + 10) (6x – 3 – 4x – 13) ≥ 0

= (10x + 10) (2x – 16) ≥ 0

= 10x + 10 = 0 atau 2x – 16 = 0

10x = -10 2x = 16

x = -1 x = 8

HP {–1,8}