Matematika

Pertanyaan

selesaikanlah pertidaksamaan nilai mutlak berikut
*2<|2-x/2|<3
*|x+5| < |1-9x|
tolong guys!!!!!

1 Jawaban

  • 2 < |2-x/2| < 3
    2 < 2-x/2 < 3
    _____________×2
    4 < 2-x < 6
    4 - 2 < -x < 6 - 2
    2 < -x < 4
    -2 < x < -4

    |x+5| < |1-9x|
    √(x+5)^2 < √(1-9x)^2
    (x+5)^2 < (1-9x)^2
    x^2 + 10x + 25 < 1 - 18x + 81x^2
    x^2 - 81x^2 + 10x + 18x + 25 - 1 > 0
    -80x^2 + 28x + 24 > 0
    80x^2 - 28x - 24 = 0
    __________________: 4
    20x^2 - 7x - 6 = 0

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