Himpunan penyelesaian |2x-4| - |x+6| =0

Bab Nilai Mutlak
Matematika SMA Kelas X

|2x - 4| - |x + 6| = 0
|2x - 4| = |x + 6|

2x - 4 = x + 6
2x - x = 6 + 4
x = 10

2x - 4 = - x - 6
2x + x = -6 + 4
3x = -2
x = -2/3

HP = { -2/3, 10 }

Materi : Persamaan Mutlak

Pembahasan :
|2x - 4| - |x + 6| = 0
|2x - 4| = |x + 6|
(2x - 4)² = (x + 6)²
(2x - 4)² - (x + 6)² = 0
(2x - 4 + x + 6)(2x - 4 - x - 6) = 0
(3x + 2)(x - 10) = 0
x = -2/3
x = 10

Hp : {-2/3 , 10}