Cari pertidaksamaan nilai mutlak a. 3 |x-1| >1 b. 2 |x-1| < 7

Materi : Pertidaksamaan Mutlak

Pembahasan :
3|x - 1| > 1
|x - 1| > 1/3
(x - 1)² > (1/3)²
(x - 1)² - (1/3)² > 0
(x - 1 + 1/3)(x - 1 - 1/3) > 0
(x - 2/3)(x - 4/3) > 0

Hp : {x < 2/3 atau x > 4/3}

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2|x - 1| < 7
|x - 1| < 7/2
(x - 1)² < (7/2)²
(x - 1)² - (7/2)² < 0
(x - 1 + 7/2)(x - 1 - 7/2) < 0
(x + 5/2)(x - 9/2) < 0

Hp : {-5/2 < x < 9/2}