tentukan himpunan penyelsaian dari persamaan berikut A). |9 - 4x| = 5 B). |x + 3| + |3x - 1| = 4

Materi : Persamaan Mutlak

Pembahasan :
|9 - 4x| = 5
(9 - 4x)² = 5²
(9 - 4x)² - 5² = 0
(9 - 4x + 5)(9 - 4x - 5) = 0
(14 - 4x)(4 - 4x) = 0
x = 7/2
x = 1

Hp : {1 , 7/2}

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|x + 3| + |3x - 1| = 4

x + 3 + 3x - 1 = 4
4x + 2 = 4
4x = 2
x = 1/2

x + 3 + 3x - 1 = -4
4x + 2 = -4
4x = -6
x = -3/2 ——» TM

-(x + 3) + 3x - 1 = 4
-x - 3 + 3x - 1 = 4
2x - 4 = 4
2x = 8
x = 4 ———» Tidak memenuhi

x + 3 - (3x - 1) = 4
x + 3 - 3x + 1 = 4
-2x + 4 = 4
2x = 0
x = 0

Hp = {0 , 1/2}