Matematika

Pertanyaan

1) | x +4 | <6
2 | 3x -1 | >8
3) | x+3| < | 2x -3|

1 Jawaban

  • No. 1
    | x +4 | <6
    -6 < x + 4 < 6
    -6 - 4 < x < 6 - 4
    -10 < x < 2

    HP : {x| -10 < x < 2}

    No. 2
    | 3x -1 | >8
    (i)
    3x - 1 > 8
    3x -1 + 1 > 8 + 1
    3x > 9
    x > 3
    (ii)
    3x - 1 < -8
    3x - 1 + 1 < -8 + 1
    3x < -7
    x < -7/3
    HP : {x| x < -7/3  atau  x > 3}

    No. 3
    |x + 3| < | 2x - 3 |
    (x + 3)
    ² < (2x - 3)²
    x² + 6x + 9 < 4x² - 12x + 9
    4x² - 12x > x² + 6x
    3x² - 18x > 0
    3x(x - 6) > 0

    + + + + +    - - - - - - - -    + + + + +
    _______0__________6_______
    jadi HP : {x| x < 0  atau x > 6}

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