Tentukan Hp dari nilai mutlak dibawah ini ( pakai rumus yang cepet paham )
a.) 2 I3xI - 4 I 2x -3 I = 8
b.) 2 I 3x +2 I > I 4x + 3 I
a.) 2 I3xI - 4 I 2x -3 I = 8
b.) 2 I 3x +2 I > I 4x + 3 I
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Materi : Persamaan dan Pertidaksamaan MutlakPembahasan :
2|3x| - 4|2x - 3| = 8
|6x| - |8x - 12| = 8
|6x| = 8 + |8x - 12|
(6x)² = (8 + 8x - 12)²
(6x)² = (8x - 4)²
(8x - 4)² - (6x)² = 0
(8x - 4 - 6x)(8x - 4 + 6x)
(2x - 4)(14x - 4) = 0
x = 2
x = 2/7
Hp : {2/7 , 2}
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2|3x + 2| > |4x + 3|
|6x + 4| > |4x + 3|
(6x + 4)² > (4x + 3)²
(6x + 4)² - (4x + 3)² > 0
(6x + 4 + 4x + 3)(6x + 4 - 4x - 3) > 0
(10x + 7)(2x + 1) > 0
x < -7/10 atau x > -1/2
Hp : {x < -7/10 atau x > -1/2}