tentukan himpunan penyelesaian persamaan berikut a. |8-2x|+x-5=0 b. |3x-5|-|10x-2|+|2x-8|=0

Materi : Persaaman Mutlak

Pembahasan :
|8 - 2x| + x - 5 = 0
|8 - 2x| = 5 - x
(8 - 2x)² = (5 - x)²
(8 - 2x)² - (5 - x)² = 0
(8 - 2x + 5 - x)(8 - 2x - 5 + x) = 0
(13 - 3x)(3 - x) = 0
x = 3
x = 13/3

Hp : {3 , 13/3}

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|3x - 5| - |10x - 2| + |2x - 8| = 0
|3x - 5| + |2x - 8| = |10x - 2|
(3x - 5 + 2x - 8)² = (10x - 2)²
(5x - 13)² = (10x - 2)²
(10x - 2)² - (5x - 13)² = 0
(10x - 2 + 5x - 13)(10x - 2 - 5x + 13) = 0
(15x - 15)(5x + 11) = 0
x = 1
x = -11/5

Hp : {-11/5 , 1}