Hitunglah nilai x (jika ada) yang memenuhi persamaan nilai mutlak berikut. jika tidak ada nilai x yang memenuhi , berikan alasanmu. a) |4-3x| = |-4| b) 2 |2x -8

Mapel : Matematika
Kelas : X SMA
Bab : Mutlak

Pembahasan :
|4 - 3x| = |-4|
|4 - 3x| = 4

4 - 3x = 4
4 - 4 = 3x
3x = 0
x = 0

4 - 3x = -4
3x = 4 + 4
3x = 8
x = 8/3

Hp : {0 , 8/3}

————————————————
2|2x - 8| = 10
|2x - 8| = 5

2x - 8 = 5
2x = 13
x = 13/2

2x - 8 = -5
2x = 3
x = 3/2

Hp : {3/2 , 13/2}

————————————————
2x + |3x - 8| = -4
|3x - 8| -4 - 2x
(3x - 8)² = (-4 - 2x)²
(3x - 8)² - (-4 - 2x)² = 0
(x - 12)(5x - 4) = 0
x = 4/5
x = 12

Hp : {4/5 , 12}

————————————————
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}

————————————————
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}