Nilai x yang memenuhi pertidaksamaan |5x + 9| > |2x + 3| adalah…

|5x + 9| > |2x + 3|
(5x + 9)² > (2x + 3)²
25x² + 90x + 81 > 4x² + 12x + 9
25x² – 4x² + 90x – 12x + 81 – 9 > 0
21x² + 78x + 72 > 0 ( dibagi 3 )
7x² + 26x + 24 > 0
D = 26² – 4(7)(24)
D = 676 – 672
D = 4
√D = √4 = 2

x1,2 = ( -b ± √D )/2a
x1,2 = (-26 ± 2)/(2×7)
x1,2 = ( -26 ± 2)/14
x1 = (-26+2)/14 = -24/14 = -12/7
x2 = (-26-2)/14 = -28/14 = -2

hp = { -2 < x < -12/7 }