tentukan himpunan |3-2x| >|x-4|

Bab Nilai Mutlak
Matematika SMA Kelas X

| 3 - 2x | > | x - 4 |

(3 - 2x)² > (x - 4)²
(3 - 2x)² - (x - 4)² > 0
(3 - 2x + x - 4) (3 - 2x - x + 4) > 0
(-x - 1) (-3x + 7) > 0
(x + 1) (3x - 7) > 0
x + 1 < 0
x < -1

3x - 7 > 0
3x > 7
x > 7/3

HP = { x | x < -1 atau x > 7/3, x ∈ bilangan real }