HP dari |6-3x| < |2x-3|

Bab Nilai Mutlak
Matematika SMA kelas X

|6 - 3x| < |2x - 3|

(6 - 3x)² < (2x - 3)²
(6 - 3x)² - (2x - 3)² < 0
(36 - 36x + 9x²) - (4x² -12x + 9) < 0
36 - 36x + 9x² - 4x² + 12x - 9 < 0
5x² - 24x + 27 < 0
(5x - 9) (x - 3) < 0
5x - 9 = 0    atau  x - 3 = 0
5x = 9                  x = 3
x = 9/5 

9/5 < x < 3

HP = { x | 9/5 < x < 3, x ∈ bilangan real }