9 < |1/2×+4| = ..............

Materi : Pertidaksamaan Mutlak

Pembahasan :
|1/2x + 4| > 9

1/2x + 4 < -9
1/2x < -9 - 4
1/2x < -13
x < -26

1/2x + 4 > 9
1/2x > 5
x > 10

Hp : {x < -26 atau x > 10, x € R}

Bab Nilai Mutlak
Matematika SMA kelas X

9 < |1/2 . x + 4|
|1/2 . x + 4| > 9

(1/2 . x + 4)² > 9²
(1/2 . x + 4)² - 9² > 0
(1/2 . x + 4 + 9) (1/2 . x + 4 - 9) > 0
(1/2 . x + 13) (1/2 . x - 5) > 0
1/2 x + 13 < 0           atau        1/2 . x - 5 > 0
1/2 x < -13                               1/2 . x > 5
x < -26                                      x > 10

HP = { x | x < -26 atau x > 10, x ∈ bilangan real }