Tentukan nilai X yang memenuhi nilai mutlak berikut a. |4x+3|=7 b. |3x-8|=4 c. 5|2x-1|-4=11 d. 2|3x-6|-2=15 e. 2|x-5|+7=14 f. 4|3x+1|-7=16 g. 3-|4x-5|=-15

Mapel : Matematika
Kelas : X SMA
Bab : Mutlak

Pembahasan :
|4x + 3| = 7
(4x + 3)² - 7² = 0
(4x + 10)(4x - 4) = 0
x = -5/2
x = 1

Hp : {-5/2 , 1}

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|3x - 8| = 4
(3x - 8)² - 4² = 0
(3x - 12)(3x - 4) = 0
x = 4
x = 4/3

Hp : {4/3 , 4}

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5|2x - 1| - 4 = 11
5|2x - 1| = 15
|2x - 1| = 3
(2x - 1)² - 3² = 0
(2x + 2)(2x - 4) = 0
x = -1
x = 2

Hp : {-1 , 2}

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2|3x - 6| - 2 = 15
2|3x - 6| = 17
|3x - 6| = 17/2
(3x - 6)² - (17/2)² = 0
(3x - 6 + 17/2)(3x - 6 - 17/2) = 0
(3x + 5/2)(3x - 29/2) = 0
x = -5/6
x = 29/6

Hp : {-5/6 , 29/6}

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2|x - 5| + 7 = 14
2|x - 5| = 7
|x - 5| = 7/2
(x - 5)² - (7/2)² = 0
(x - 5 + 7/2)(x - 5 - 7/2) = 0
(x - 3/2)(x - 17/2) = 0
x = 3/2
x = 17/2

Hp : {3/2 , 17/2}

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4|3x + 1| - 7 = 16
4|3x + 1| = 23
|3x + 1| = 23/4
(3x + 1)² - (23/4)² = 0
(3x + 1 + 23/4)(3x + 1 - 23/4) = 0
(3x + 27/4)(3x - 19/4) = 0
x = -9/4
x = 19/12

Hp : {-9/4 , 19/12}

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3 - |4x - 5| = -15
|4x - 5| = 18
(4x - 5)² - 18² = 0
(4x + 13)(4x - 23) = 0
x = -13/4
x = 23/4

Hp : {-13/4 , 23/4}