Tentukan pertidaksamaan nilai mutlak = |2x - 3| < |4x + 5|

NiLai MutLak

|2x - 3| < |4x + 5|
(2x - 3)² - (4x + 5)² < 0

▶ A² - B² = (A + B)(A - B)
Misal : A = (2x - 3) ; B = (4x + 5)

(6x + 2)(-2x - 8) < 0
x = -1/3 ; x = -4

Nilai x yg memenuhi :
x < -4 atau x > -1/3

|2x - 3| < |4x + 5|
( 2x - 3 )² < ( 4x + 5 )²
( 2x - 3 )² - ( 4x + 5 )² < 0

( 2x - 3 + 4x +5 ) ( 3x - 3 -(4x + 5) ) < 0
( 6x + 2 ) ( 3x -3 -4x - 5 ) < 0
( 6x + 2 ) ( -x - 8 ) < 0

x pembuat nol
6x + 2 = 0
6x = -2
x = -2/6

-x - 8 = 0
-x = 8
x = -8