Hitunglah nilai x yang memenuhi persamaan nilai mutlak berikut A. 2|3x-8| = 10 B. 5|2x-3| = 2|3-5x| C. 2x + |8-3x| = |x-4|

Mapel : Matematika
Kelas : X SMA
Bab : Mutlak

Pembahasan :
2|3x - 8| = 10
|3x - 8| = 5

3x - 8 = 5
3x = 13
x = 13/3

3x - 8 = -5
3x = 3
x = 1

Hp : {1 , 13/3}

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2x + |8 - 3x| = |x - 4|
|x - 4| - |8 - 3x| = 2x

x - 4 - 8 + 3x = 2x
4x - 12 = 2x
4x - 2x = 12
2x = 12
x = 6

x - 4 - 8 + 3x = -2x
4x - 12 = -2x
4x + 2x = 12
6x = 12
x = 2

Hp : {2 , 6}

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5|2x - 3| = 2|3 - 5x|
(10x - 15)² = (6 - 10x)²
(10x - 15)² - (6 - 10x)² = 0
(10x - 15 + 6 - 10x)(10x - 15 - 6 + 10x) = 0
(-9)(20x - 21) = 0
-180x + 189 = 0
180x = 189
x = 189/180
x = 21/20

Hp = {21/20}