|2×-3|<|×+4|= mohon bantuanya....

Bab Nilai Mutlak
Matematika SMA Kelas X

|2x - 3| < |x + 4|

(2x - 3)² < (x + 4)²
(2x - 3)² - (x + 4)² < 0
(2x - 3 + x + 4) (2x - 3 - x - 4) < 0
(3x + 1) (x - 7) < 0
3x + 1 = 0          atau           x - 7 = 0
3x = -1                                 x = 7
x = -1/3

+ + +     - - - - - - - - - - -   + + + + 
----------------------------------------------
         -1/3                      7

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

Materi : Pertidaksaman Mutlak

Pembahasan :
|2x - 3| < |x + 4|
(2x - 3)² < (x + 4)²
4x² - 12x + 9 < x² + 8x + 16
3x² - 20x - 7 < 0
(3x + 1)(x - 7) < 0

Hp : {-1/3 < x < 7, x € R}