himpunan penyelesaian dari |2x-1| = |x+3|

Bab Nilai Mutlak
Matematika SMA Kelas X

|2x - 1| = |x + 3|

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

2x - 1 = - (x + 3)
2x - 1 = - x - 3
2x + x = -3 + 1
3x = - 2
x = -2/3

HP = { -2/3, 4 }

Materi : Persamaan Mutlak

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

Hp : {-2/3 , 4}