tentukan himpunan penyelesaian dari: 1. 2 | x | + 1 = 5 2. | 5x + 3 | = | 2x | 3. 4 | x-2 | = 8 4. 2 - | x-2 | = x Mohon Bantuannya

Mapel : Matematika
Kelas : X SMA
Bab : Mutlak

Pembahasan :
2|x| + 1 = 5
2|x| = 4
|x| = 2

Maka x = -2 atau x = 2

Hp : {-2 , 2}

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|5x + 3| = |2x|
(5x + 3)² = (2x)²
(5x + 3)² - (2x)² = 0
(3x + 3)(7x + 3) = 0
x = -3/7
x = -1

Hp : {-3/7 , -1}

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4|x - 2| = 8
|x - 2| = 2
(x - 2)² - 2² = 0
x(x - 4) = 0
x = 0
x = 4

Hp : {0 , 4}

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2 - |x - 2| = x
|x - 2| = 2 - x
(x - 2)² = (2 - x)²
(x - 2)² - (2 - x)² = 0
2x - 4 = 0
2x = 4
x = 2

Hp : {2}